From my understanding, both of them refer to the ability to plastically deform without failure. Can any expert explain to me? Thank you very much
Ductility is simply the strain to fracture (measured as the % elongation in a uniaxial tensile test, of the reduction in area - it is the "extendability" of the material (for want of a better word). The toughness of a material, conversely, is its resistance to fracture, which can be defined in terms of fracture mechanics parameters or more simply in energy terms - one simple definition is that it is the area under the stress- strain curve, or work to cause fracture. Toughness and ductility, however, are not the same properties, although they are often related. For example, lead solder has excellent ductility but you wouldn't call it tough. A high-carbon tool steel, on the other hand, can be very strong, or hard, but would never be regarded as tough. Toughness relies on a combination of strength and ductility. As in many classes of materials, these two properties tend to be mutually exclusive, the generation of toughness in a material is often a compromise. For further thoughts on these issues, you might wish to glance at by article in Nature Materials in 2011 on "The Conflicts between Strength and Toughness" (vol. 10, p. 817, Nov. 2011).
Ductility is simply the strain to fracture (measured as the % elongation in a uniaxial tensile test, of the reduction in area - it is the "extendability" of the material (for want of a better word). The toughness of a material, conversely, is its resistance to fracture, which can be defined in terms of fracture mechanics parameters or more simply in energy terms - one simple definition is that it is the area under the stress- strain curve, or work to cause fracture. Toughness and ductility, however, are not the same properties, although they are often related. For example, lead solder has excellent ductility but you wouldn't call it tough. A high-carbon tool steel, on the other hand, can be very strong, or hard, but would never be regarded as tough. Toughness relies on a combination of strength and ductility. As in many classes of materials, these two properties tend to be mutually exclusive, the generation of toughness in a material is often a compromise. For further thoughts on these issues, you might wish to glance at by article in Nature Materials in 2011 on "The Conflicts between Strength and Toughness" (vol. 10, p. 817, Nov. 2011).
Thank you Dr.Robert. So, does it mean a material which has a high strength and high ductility can be considered as high toughness material? Since high strength together with high ductility will have large area under the stress-strain curve.
Toughness is the ability of the material to plastically deform before fracture, while ductility is the measure of how much something deforms plastically before fracture. Toughness is measured through strength and ductility. The higher the strength, and the ductility of the metal is, the more tough it is. So, to answer your last question, yes, material which has a high strength and high ductility can be considered as high toughness material.
I'm still confused because some of the research work mentioned thermoplastic has high toughness compared to thermoset. Is it correct? Is this related to its dynamic effect and differential hardening?
Thermosetting and thermoplastic plastics have different properties. When we heat thermoplastic they deform easily i.e. there is some kind of flow within material similar to ductility behaviour. But thermoset, having brittle nature thus they don't have chances to deform they break when an external load is applied to them. Now, if we are talking about toughness property
Now, if we are talking about toughness property it is the property it is the area under the stree-strain curve (as Dr Robert O Ritchie) said. Now u can think how material (plastics) behave under the tensile curve and your confusion may be cleared.
Thank you everyone. So, generally the larger the area under the curve, the greater the impact properties and hence the better the toughness properties of a material. It all depends on the area under stress-strain curve. Although there are some external factor such as temperature (like Mr.Niazi said) that will influence the toughness properties but the factor is small enough during testing. Am I right?
we define Toughness on the basis of energy being absorbed during elongation until fracture-usually calculated by the area under the stress-strain curve.
Ductility is measured by the total elongation of the material till fracture,it is also determined from strain at failure
Dr. Niazi:
My apologies but I beg to differ. Although the toughness of a material is certainly best defined in terms of fracture mechanics methodologies, at least where fracture evolves from the propagation of a self-similar crack (and not from widely distributed damage), from a materials development perspective it is perfectly reasonable to assess the toughness from the area under the stress/strain curve as an indicator of a tough or brittle material. This approach is widely used in the Biomaterials and Chemistry literature, for example, as a measure of the toughness in their materials. Naturally for engineering structural design, it is much wiser to employ fracture mechanics with a highly constrained cracked sample to provide a worst-case fracture toughness in terms of a stress intensity, J-integral, or equivalent, but for the general assessment of the mechanical properties of materials, the stress-strain curve can certainly be used to provide an assessment of toughness.
ROR
In general, ductility is a function of strain only, wheareas toughness is a function of both stress and strain. Thus the area under the stress-strain curve is a measure of toughness, while the % elongation (on the strain axis) is a measure of ductility. Both ductility and toughness depend on the structure of the material which is influenced both temperature and pressure (or stress or load).
Dr. Niazi:
OK, but impact and strain rate represent other issues. There is absolutely nothing to say that toughness must be measured in impact. One can clearly measure the area under a stress-strain curve for a high strain rate tensile test, or in the same manner perform a high strain rate fracture mechanics test (or notched test, such as the Charpy test); again both are respectable measures of the toughness. Impact loading is simply a particular loading mode which, if relevant, can be used to assess the toughness.
ROR
Dr. Robert:
1.why 'strength and toughness are mutually exclusive' in most materials? is the strength refer to yield strength more specific?
2.tensile strength or fracture strength which get in uniaxial tensile test seems not independent of toughness .
3.high fracture toughness means high fracture resistance for existing crack sample or component. however, for brittle or ductile material and component,there is no existing crack or defect in some applications,high fracture strength of brittle material or tensile strength of ductile material(both get in in uniaxial tensile test ) seems to represent fracture resistance more appropriate .
thanks for your comments.
Dear Hou:
I will attempt to address each of your questions:
1. 'Strength and toughness are mutually exclusive' in most materials because one of the principal contributions to toughness is plasticity (at least for intrinsically toughened materials). In simplistic terms, high strength means less plasticity, smaller plastic zones to blunt cracks, higher stresses at the tip of a crack (which scale with the flow stress) to promote fracture, less relaxation of these stresses from plasticity - all of which diminish the resistance to fracture. Ideally for toughness one needs both high strength and high ductility, but that often involves a compromise for the development of damage-tolerant materials. (Incidentally, in this form of discussion in terms of generalizations, strength refers to the flow strength, which can be the yield or tensile strength.)
2. The tensile strength and flow strength are not necessarily independent of the toughness - strength is a contributing factor - but so is the ductility which is often inversely related to strength. Actually, simple models for the toughness in energy terms of a brittle material scale inversely with strength whereas for a ductile material the energy toughness generally scales with the ductility x the flow strength (x a characteristic length parameter which is related to some multiple of the particle spacing or grain size). As strength and ductility tend to be mutually exclusive properties and toughness depends on both strength and ductility, this is the origin of the observations that strong (hard) materials are in generally far less fracture resistant than lower strength ones. Indeed, if you look through the last 150 years of structural engineering, there are countless examples of engineers choosing stronger materials for safety critical applications only to find that they are much more prone to fracture (often without warning). A prime example is metallic airframes (the fuselage) for aircraft. Are highest strength peak aged aluminum alloys used? Generally not as they're more prone to fracture, fatigue and stress corrosion. For this reason, somewhat lower strength under or overaged aluminum alloys are generally used.
If you wish to read further on this, most textbooks on Fracture address these issues. From my own work, the following two articles are expressly devoted to this topic:
- R. O. Ritchie and A. W. Thompson, "On Macroscopic and Microscopic Analyses for Crack Initiation and Crack Growth Toughness in Ductile Alloys," Metallurgical Transactions A, vol. 16A (2), Feb. 1985, pp. 233-248.
- R. O. Ritchie, “The Conflicts between Strength and Toughness”, Nature Materials, vol. 10 (11), Nov. 2011, pp. 817-822.
3. These comments though apply to all materials whether or not you believe that they contain a crack. In structural engineering, there is no such thing as a defect-free or crack-free material or component. Every material contains defects - that's not the issue - it's how large (and hence how dangerous) these cracks or defects are. For example, most aerospace and nuclear components are designed on the presumption of pre-existing defects; the projected life is then estimated in terms of how long, or how many fatigue cycles, it will take for such cracks to grow to critical size where they can cause outright fracture (at the fracture toughness) or limit-load failure (when the stress in the remaining ligament exceeds the strength - with allowance for the effect of constraint). This is the basis of damage-tolerant design which ideally should be used for all safety-critical structures and components.
I hope that you find these brief comments useful.
ROR
Dr. Niazi,
you mean when we mention toughness, we have to specified into impact toughness and so on?
Dr.Robert:
1. In your paper "Evaluation of Toughness in AISI 4340 Alloy Steel Austenitized at Low and High Temperatures, p835" , the fracture toughness equation[3]&[4] seems not include plasticity term.
2. It's inevitable that material will contain defects. by material testing ,e.g. uniaxial tensile test, obtains fracture strength value. the fracture strength value perhaps is not material's true strength because of the inevitable defects in testing material.
thank you very much .
Dear Hou:
1. The paper to which you refer, by Ritchie, Francis, & Server, which incidentally was written 40 years ago, refers to a critical stress model for fracture. Plasticity is not explicitly included in the toughness relation - this seems appropriate as the analysis was performed for an ultrahigh strength steel - but plasticity is included in the definition of the crack tip stress and deformation fields. The purpose of this paper was to explain some strange effects that when the prior austenite grain size is coarsened, the sharp crack KIc toughness is enhanced yet the blunt notch Charpy toughness is degraded - which is related to a statistical effect.
2. Defects have an inevitable presence in materials. The fracture strength that you measure is certainly the true fracture strength. You have to test a sufficiently large number of samples to make sure that you end up with a statistically relevant value.
Cheers
ROR
I think, Professor R. O. Ritchie explained very well the subject.
It is clear now.
Thank you for your effort.
E.B
Prof Robert O Ritchie
Can you suggest any article to understand Crack Initiation and Crack Growth phenomena in FRPs under low-velocity impacts ?
One cannot put it better than Robert for what we know at present, so I can only flag up his answers. I just wanted to add that we do not know all relations yet to answer the question about possible link between ductility and toughness. As long as the toughness is considered a separate material property of its own right (as we teach students in fracture mechanics) we will not have a clear answer. If we devise a way to derive this property from parameters describing deformation, say true stress-strain curve of a tensile specimen, with the addition of microstructure characteristics, we might be closer to an answer.
Dear Dr. Rawat:
I'm afraid that fiber reinforced plastics (FRPs) are not really my area of expertise. I have worked on impact damage of metals, principally titanium alloys, as it pertains to foreign object damage in turbine blades and there our analyses was based entirely on the initiation of small cracks at the impact sites and whether they would subsequently propagate under the applied loads (or stress intensities) that the turbine blades were subjected to.
To my knowledge, I do not believe that such a fracture mechanics-based analysis has been done for the impact damage of FRPs but, as I mentioned above, I am not an expert in these composite materials and so I may well be wrong.
If you're interested in how we handled the subsequent effects of impact damage in terms of the initiation and propagation of small cracks, you might wish to look at:
J. O. Peters, et al. On the Application of the Kitagawa-Takahashi Diagram to Foreign-Object Damage and High-Cycle Fatigue, Engin. Fract. Mech., 69, 2002, 1425-46.
B. L. Boyce, et al., Mechanical Relaxation of Localized Residual Stresses Associated with Foreign Object Damage, Mater. Sci. Eng. A, 349, 2003, 48-58.
Sincerely
ROR
Dear Prof Robert O Ritchie,
Thank you so much for your reply and suggestions.
The judgement "...both of them refer to the ability to plastically deform without failure..." is ABSOLUTELY WRONG, as ductility and toughness describe ABSOLUTELY DIFFERENT physico-mechanical properties of solids. Concerning the toughness of ceramics and composites, please, see the handouts of my lectures on Materials Science & Engineering for Physics students
https://www.researchgate.net/publication/275271377_Ceramic_Materials_Science_Engineering_Part_3_-_Physical_Properties
on my ResearchGate account.
Research Ceramic Materials Science & Engineering (Part 3 - Physical Properties)
Dear Dr. Robert
1. Material or component need enough Fracture Toughness, how to determine how much toughness is required in application?
2. Why people are pursuing and researching high or ultrahigh strength steel in aerospace and automobile industry ,rather than high or ultrahigh toughness steel if high toughness is more resistant to fracture?
3. Is statistical effect more obvious in fracture toughness test than uniaxial tensile test?In papers, one uniaxial tensile test sample usually can represent the strength of material or component . if the strength is high in the uniaxial tensile test and can assure no defects produced after testing ,can this high strength mean high fracture resistance?
Thank you very much.
Dear Prof. Hamed Mirzadeh,
Sorry, but writing the sentence "...Toughness is the ability to absorb energy in the plastic range (?)..." you have made a principal mistake, as it is clear for everybody that, for a example, the wooden materials don't demonstrate any evidence of plasticity, though they always have a certain level of toughness (sometimes it is very high!). The similar situation is with many types of ceramics and composites developed and studied in the last half-century. Please, see my publications on hetero-modulus ceramic-ceramic composites (dated from 1970s up to date) on ResearchGate account. Thus, the definition should be formulated as "Toughness is the ability to absorb and dissipate the fracture energy by various ways such as plastic deformation in ductile stuffs, fibre pull-out in fibre-reinforced composites and some others".
With my best wishes,
Igor
Both Hamed and Igor are right. different definitions can be accepted based on metallic or ceramic materials.
Cheers
Mostafa
However, plastic deformation is also inherent to ceramics..., in the same (!) characteristic temperature range corresponding to their melting points..., the only difference (!). All the refractory metals (please see chapters on W, Re, Os, Ta, Mo, Nb and Ir from my UHTM-I book on ResearchGate account) are rather brittle (no tough enough!) at lower temperatures. So, in the 21st century we have to use General Materials Science Theory and consider metals, ceramics and polymers jointly and formulate joint/general definitions.
Best wishes and regards to everybody,
Igor
Dr. Robert :
In the cleavage fracture stress calculation, there is a item plastic work γ_p :
how it form?
Which factors can influence the γ_p value? In articles, its value is either 14 or 200 J/m2.
The critical step is usually the grain boundary ,then how grain boundary influence or produce the γ_p value?
Dr. Hou:
This is a good question. The plastic work term is not easy to quantitatively estimate. In our study on low carbon steels, we used the value determined by Gerberich and Kurman in their 1985 Scripta Metallurgica paper (vol. 19, p. 295). That was the most accurate and recent measurement at the time that we performed our statistical analysis of the fracture of these steels, although other, somewhat lower, values were in the literature before that. The precise value of this term will depend naturally upon the critical step involved in the fracture. As you state, this energy will be different for fracture controlled by the initiation cracking of the carbide, compared to that controlled by the propagation of this crack into the matrix or at somewhat higher temperatures by the propagation of the crack through the subsequent ferrite grain boundary. There is a reasonable discussion of this issue in the beginning of the paper by Lin et al., Stochastic modelling of the independent roles of particle size and grain size in transgranular cleavage fracture, Metall. Trans. A, 18A (5), 641-51, April 1987.
ROR
Dr. Hou:
In principle, yes - the γ_p value is the effective energy for fracture and as such includes contributions from such factors as the surface energy and the plastic work term. It is thus a measure of the intrinsic toughness of the material (effectively equal to the critical value of the strain energy release rate at fracture) and thus will be affected by all factors which influence that toughness, most specifically the microstructure; this would of course including carbon content, tempering temperature, and forth. However, it is used mostly in Griffith-type models, rather than as a measurable evaluation of toughness. If the latter is your intent, you are better served by following conventional fracture mechanics approaches by measuring, for example, the critical stress intensity for fracture.
ROR
Dr. Hou:
Depending on what temperature range you're at, which determines the critical fracture event, the critical cleavage fracture stress will be principally dependent upon the (i) flow stress (if the critical event is a dislocation pile-up to generate a crack, i.e., nucleation controlled), (ii) the size, shape and fracture strength of the carbide (or whatever is the relevant particle is) to generate a running crack that can propagate through the particle into the ferrite grain, and/or (iii) the grain size and grain-boundary strength (which controls whether the crack can propagate through the next boundary (the latter two critical steps are propagation controlled). It is also controlled by the temperature although most data show a relatively weak dependence. The tensile strength of a ductile steel is very likely to the lower than the fracture stress but it is somewhat difficult to be certain; it is more certain that the yield strength will be lower. However, comparing the tensile strength to the fracture strength is tricky; the tensile strength is an engineering stress, i.e., the maximum load divided by the initial cross-sectional area, whereas the fracture strength is a true stress, i.e., the fracture load divided by the instantaneous area, and so one cannot be certain unless one knows the actual reduction in area at fracture.
ROR
Dr.Robert :
If nucleation controlled, what factors may influence the nucleation stress and how they influence?
If the material is ductile fracture, any flow stress from deformation to fracture shoud be lower than cleavage stress, otherwise it will be cleavage rather than ductile.
For the initiation controlled mechanisms of cleavage fracture in steels, which tend to occur at the lowest temperatures, the critical step is a dislocation pile-up typically at a (grain-boundary) carbide particle. The nucleation stress under these circumstances is effectively the flow stress, i.e., the yield stress, and so all the factors that affect yield, e.g., temperature, composition, etc., will affect this nucleation stress for fracture.
With respect to ductile fracture, remember that this is a (stress-state modified) strain-controlled fracture. In simple terms, the transition to ductile fracture occurs when the development of tensile stresses at a crack tip, which scale with the flow stress and thus are further enhanced by strain hardening, are insufficient (as the strength is decreasing with increasing temperature) to exceed the critical fracture strength for (stress-controlled) brittle fracture. Under such circumstances, the critical strain for ductile fracture is exceeded first and mechanisms such as microvoid coalescence ensue. Thus you're correct, for ductile fracture the flow stress will be lower than the cleavage fracture stress.
ROR
Dr.Robert:
1. Professor knott said in Quantifying the quality of steel ,“The stress level can be raised by strain-hardening, but this requires high plastic strains in the crack-tip region, which blunt-out microcrack nuclei (and, of course, increase the CTOD). This makes it increasingly difficult to propagate cleavage microcracks.”
Is it possible cleavage fracture occur after large amount of elongation in the uniaxial tension test of intact sample if the flow stress reach its cleavage strength?
2. as-quenched medium and high carbon martensite have high hardness and strength, but have low tensile or bending strength.Some books say they are brittle in tensile ,so its strength cann’t get. I think brittle fracture is the normal mode in tenisile for as-quenched medium and high carbon martensite, and the frcture strength represent Its strength that resist tensile.Do you think the fracture strength represent cleavage strength or brittle fracture strength in this case?
Dr. Hou:
In answer to your first question, yes definitely. John Knott stated it very precisely.
In response to your second question, as-quenched medium and high carbon steels tend to be exceedingly hard, but with correspondingly low toughness with their untempered martensitic structure which can be exceedingly brittle. Whether you call it the cleavage strength or the brittle fracture strength, it will be low for these systems. Untempered medium to high carbon steels in their as-quenched state are very hard yet very brittle. Without subsequent tempering, they are not very appropriate for most, if not all, structural applications.
ROR
Professor Ritchie:
1. In tensile of intact sample , assuming the flow stress reach cleavage stress after yielding and plastic deformation . Crack form before reaching cleavage stress,because of the whole sample has been yielding,the crack will blunt .So even though the cleavge stress attained,it cann’t extend.Do you think so?
2. As-quenched medium and high carbon martensite is very brittle,it doesn't necessarily mean low cleavage strength.There are different theories.do you think what’s the mechanism of low tensile strength or cleavage strength for As-quenched martensite?
3. And for cleavage fracture of the low temperature tempering medium and high carbon plate martensite structure,what’s controlling microstructural feature? And which factors affect the boundary strength?
I’m trying to enhance static bending strength of carbonitriding product from metallurgical aspect. Thank you very much for your comments which will help me a lot.
Dr. Hou:
To respond to your three questions:
1. In tensile of intact sample , assuming the flow stress reach cleavage stress after yielding and plastic deformation . Crack form before reaching cleavage stress,because of the whole sample has been yielding,the crack will blunt .So even though the cleavage stress attained,it can’t extend.Do you think so?
Once one is at a temperature above the nucleation-controlled regime, cracks can readily form in carbide particles and/or ferritic grains that are of insufficient length (or extending at sufficient velocity) to propagate, respectively, out pf the particle into the ferrite grain or through the next grain boundary - in Morris Cohen's original description, these features are "exhausted". What this means is that many nucleated cracks in particles or grains may not be severe enough to result in catastrophic fracture - they blunt out and play no further role in the process of fracture. It just takes one (or perhaps a small number of) critical cracks in these features to set off catastrophic fracture. Although the onset of cleavage fracture is nominally "weakest link", many such cracks form in carbides and grains but are not critical and thus play no further part in the macroscopic fracture process. So your description is reasonably accurate.
2. As-quenched medium and high carbon martensite is very brittle,it doesn't necessarily mean low cleavage strength.There are different theories.do you think what’s the mechanism of low tensile strength or cleavage strength for As-quenched martensite?
3. And for cleavage fracture of the low temperature tempering medium and high carbon plate martensite structure,what’s controlling microstructural feature? And which factors affect the boundary strength?
To answer both question 2 and 3, in comparison to low carbon ferritic steels, there are few mechanistic models for the brittle fracture of quenched and tempered martensitic steels. The critical features controlling their toughness though are factors such as (i) the prior austenite grain size, which is a function of the austenitizing temperature, (ii) the type of martensite (plate vs. lath) formed, which can depend on carbon content, and (iii) naturally the tempering temperature, which controls the carbide size and stability, the presence and stability of any retained austenite, and any segregation of impurities to interfaces. Modeling such complex, multi-factor, coupled phenomena is distinctly difficult, which presumably accounts for the paucity of detailed mechanistic models for martensitic steels.
ROR
I’m trying to enhance static bending strength of carbonitriding product from metallurgical aspect. Thank you very much for your comments which will help me a lot.
What is the difference between toughness and ductility of a material? - ResearchGate. Available from: https://www.researchgate.net/post/What_is_the_difference_between_toughness_and_ductility_of_a_material#view=5812935cb0366dd0326f28c6 [accessed Oct 27, 2016].
Carbides and inclusions can both be the source of initiating fracture, but they do it in different ways. Generally the carbides are far more numerous, particularly in modern steels that are "cleaner" than the quality of the same steel made decades ago. They tend to actually crack when impinged by a dislocation pile-up, as their interface with the ferrite matrix is comparatively strong. In contrast, inclusions, such as oxides or MnS particles, will be far less numerous than the carbides; they generally have a comparatively weak interface with the ferrite matrix and thus tend to debond rather than fracture.
In the lower-temperature cleavage regime, the more numerous carbides and the fact that they generate a sharp crack when they fracture are two reasons that they are primarily associated with the origin of cleavage fracture, but the larger inclusions can still play a smaller, nominally similar, role.
However, at higher temperatures where plastic flow is easier, the debonding of the inclusions from the matrix can create a prime source of voids which provides the basis for strain-controlled microvoid coalescence fracture to occur. However, the ductility of steels would be much larger than is typically measured if these microvoids, created around the few inclusions, where simply allowed to simply grow until they impinge to create a total fracture. What happens is that at some stage in their growth, the material between the microvoids can "neck" through a plastic instability which generally involves strain localization along a shear band created by cracks in the smaller carbides linking up - this is generally termed "void sheet coalescence" - and can severely limit the tensile ductility of the steel. For this reason, steels with higher strain hardening tend to delay this instability and can display higher ductility and toughness (in the ductile fracture regime).
The bottom line here is that carbides and inclusions are both involved in ductile and brittle fracture, but the carbides are more numerous and tend to crack whereas the smaller volume fraction of inclusions are more likely to debond to form microvoids.
ROR
Professor Ritchie:
I have some confusions about your statement(Oct 27, 2016): “What this means is that many nucleated cracks in particles or grains may not be severe enough to result in catastrophic fracture - they blunt out and play no further role in the process of fracture. It just takes one (or perhaps a small number of) critical cracks in these features to set off catastrophic fracture. “
My confusion: For propagation controlled fracture, the critical crack can also readily form and must await the stress increasing high enough to propagate . In the waiting period, the critical crack will blunt and be “exhausted” , especially when the global stress exceed yielding strength.
Dr. Hou:
Specifically, many cracks can form, in either carbides or grains (depending upon the temperature range), which are not large enough to propagate catastrophically to result in overall brittle fracture. Often these blunt out - they become "exhausted" in Morris Cohen language, and play no further role in the overall fracture process. The largest such microcrack, or the one with sufficient velocity, to exceed the (local) critical crack size to "escape" the particle or the grain, is the one that provides the "weakest link" for overall fracture. If one looks at the microstructure, it is only a small fraction of the carbides (or at somewhat higher temperatures, the ferrite grains) that are active participants in this fracture process.
ROR
The "conflict" between strength and ductility primarily arises from the fact that the principal mechanism contributing to ductility and (intrinsic) toughness is plasticity - it, of course, acts to blunt cracks through the creation of a plastic zone at the crack tip and the plastic work associated with the motion of, for example, dislocations expends significant energy - whereas high strength is invariably accompanied primarily by lower degrees of plasticity. That's the general problem with most classes of materials but there are ways to nominally "defeat" this conflict (see Ritchie "Conflicts between strength and toughness, Nature Materials 10 (2011) 817). One means is to induce extrinsic toughening in the wake of the crack tip, through for example, crack bridging, which in many instances does not necessarily involve plasticity. With extrinsic toughening, there is no conflict between strength and toughness. Nature does this effectively with its materials, creating both mechanisms of intrinsic and extrinsic toughening. Another means, which can be very effective for metallic alloys, is to create mechanisms of continuous strain hardening, which naturally elevate the strength but at the same time suppress necking (tensile instabilities) which can dramatically increase the ductility. Indeed, this is the basis of the damage tolerance of austenitic stainless steels, CrCoNi-based high-entropy alloys, and TWIP- and TRIP-steels.
ROR
Dr. Hou:
The term γ_p is the plastic work term in the modified Griffith equation and as such is a measure of the intrinsic toughness, i.e., the work involved in fracture. The relationship between γ_p value and ductility is thus the relationship between toughness and ductility; it is one major component of the toughness along with the strength.
Grain boundaries can resist crack propagation, yes, but it very much depends on the mode of fracture. For example, the presence of grain boundaries is not too important to the progress of ductile fracture via microvoid coalescence. Furthermore, intergranular fracture, whether due to creep crack growth, stress-corrosion cracking or embrittlement by impurities or hydrogen, is naturally enhanced by the presence of such boundaries. The propagation of a cleavage fracture though is inhibited by grain boundaries as it invariably involves a separation along a crystallographic low energy plane, and therefore the fracture has to reorient itself as it encounters each grain boundary. It is for this reason that, all other things being equal, coarse-grained low carbon steels are generally more brittle than finer-grained steels below their ductile-to-brittle transition temperature.
Fatigue crack growth can also be resisted by grain boundaries but again where the path of the crack is crystallographic, as at lower stress-intensity ranges in planar-slip materials. At higher growth rates, however, where striations form due to crack advance via an alternating crack-tip blunting and resharpening, the presence of boundaries not longer appears to be that important.
The bottom line here is that grain boundaries largely affect the propagation of a crack (i) to inhibit crack advance where the crack path is crystallographic in nature, and (ii) to facilitate cracking where the crack path is intergranular (the latter statement being essentially obvious!).
ROR
Dr. Hou:
The fracture stress for most steels is relatively constant with temperature (provided the fracture mode stays essentially the same), primarily because over a large range of temperature, the critical stress for cleavage involves the rate-determining step of the fracture of carbides. As such carbides, e.g., cementite, are higher melting point compounds/intermetallics (compared to the ferrite grains), their fracture is relatively immune to temperature in this range. At the lowest temperatures though, the critical fracture event for cleavage involves the nucleation of a crack, i.e., from the pile-up of dislocations against the particle, which is controlled by the yield or flow stress of the steel at this temperature. As the yield strength will be a strong function of the temperature, the cleavage fracture strength is no longer constant in this regime. In similar fashion at higher temperatures (but still below the ductile-to-brittle transition), the critical fracture event for cleavage involves the propagation of a crack (now out of the carbide) through the ferrite grain and its next grain boundary. As this crack will now be carrying a plastic zone due to local yielding in the ferrite, the fracture stress will again become a function of temperature. For a full discussion of this, I would refer you to the attached paper.
The bottom line here is that the notion of a constant fracture stress for cleavage is only approximate. The fracture strength will be relatively constant, compared to the large change in the yield strength of the stress, because over a large temperature regime, carbide fracture controls the overall fracture event. However, at very low temperatures and temperatures closer to the ductile-to-brittle transition, where the rate-limiting steps for cleavage fracture are different, the cleavage fracture stress will likely display some temperature-dependence.
ROR
Article Stochastic modeling of the independent roles of particle siz...
Professor Ritchie:
In material ,there are defects or cracks unavoidably. In tension, those cracks or defects will extend directly when meet the Griffith criterion or will extend as your RKR model(new crack initiate ahead of exsiting crack)? The fracture strength calculations are different accordingly then.
Dr. Hou:
As the English proverb goes "There are many way to skin a cat!". Both these criteria address a similar problem, that of predicting the fracture strength or fracture toughness, but in different ways. As both are engineering approximations to reality, yes, they may yield slightly different results, and they both have their pluses and minuses.
The famous Griffith criterion is "a necessary yet insufficient criterion for fracture". It first recognized the vital role of pre-existing cracks, sets up an appropriate energy balance for fracture instability, but in quantitative terms suffers from the lack of an exact knowledge of what the effective fracture energy (plastic work term) is in real materials. In metallic materials, for example, the latter plastic work term can be several orders of magnitude larger than the surface energy (which was the energy used in the original Griffith approach) and so this criterion is clearly inappropriate for application to more ductile materials. The RKR model similarly seeks the conditions for the unstable propagation of a crack, but now incorporates nonlinear elastic solutions for the stresses and displacements at the tip of a crack in the context of fracture mechanics, and so is more directly applicable to metallic materials.
As I have shown in the attached paper, you can marry these two approaches, but they are essentially two completely separate means to predict fracture, one based on energy arguments and the other on the presence of a crack-tip field and a local fracture criterion (i.e., the attainment of a critical stress over a characteristic distance ahead of a pre-existing crack).
ROR
Article A Statistical Model of Brittle Fracture by Transgranular Cleavage
Dr. Hou:
In principle, yes, you could use a yp value and the Griffith criterion to predict if a microcrack or fatigue crack will grow. However, the Griffith is an energy criterion which is based originally on have a sufficient release of strain energy to overcome the surface energy of the new crack surface that is created. Unfortunately, even for very brittle ceramics where there will be no plasticity, such as in alumina, the yp value at fracture is still typically an order of magnitude larger than the surface energy (for metallic materials the yp value at fracture could be several orders of magnitude larger than the surface energy. So as I stated before, the Griffith criterion is "a necessary but insufficient criterion for fracture". This is the basis of why George Irwin developed continuum fracture mechanics to avoid these difficulties with what the energy actually is. The strain energy release rate simply becomes the critical value of energy to cause the onset on cracking in an nominally elastic solid - GIc (which of course can also be expressed in terms of a critical stress intensity KIc) - or in the presence of some degree of plasticity, JIc is similarly the critical value of energy to cause the onset on cracking. Under conditions of linear elasticity, of course JIc = GIc = KIc2/E, where E is the appropriate Young's modulus for plane stress or plane strain.
ROR
Professor Ritchie:
In your RKR model, the y_p value(effective fracture energy, orders of magnitude larger than the surface energy. Specific values have existed. Your last article also provide a value, 23 J/m’ ) can use in Griffith criterion of microcrack ahead of exsiting or pre-fatigue crack. I think why this y_p value and Griffith criterion cann’t be used to exsiting or pre-fatigue crack directly?
Thoughness is ability of material in enduring plastic deformation without failure (KIC) and area of stress and strain curve but ductility is ability of material in work ability e=(L-L0)/L0
In materials science and metallurgy,toughness is the ability of a material to absorb energy and plastically deform without fracturing.[1] One definition of material toughness is the amount ofenergy per unit volume that a material can absorb before rupturing. It is also defined as a material's resistance tofracture when stressed.
Toughness requires a balance ofstrength and ductility.
Dr. Hou:
I think that your latest assessment is probably correct. Models like RKR are largely conceptual and- yes - can predict toughness values, but to do this without any adjustable parameters (for want of a better word) is almost impossible for any microscale model of the fracture toughness. In the statistical version of RKR, we used the value of 23 J/m2 for the yp value as this value had just been published based on a very careful study by Gerberich for a very similar steel (and so we didn't regard it as an adjustable parameter in this particular case). The bottom line though is that these models are good for indicating mechanistic (semi-quantitative) trends, but as Mike Ashby once euphemistically described all such models, including his own, they are essentially "enlightened empiricism", i.e., you develop the model on the basis of the best physics and physical understanding that you have, but you may still have to fix the constants in the model using real materials data. When you realize that you are using physical events that occur on the micro- and submicron dimensions to predict a macroscale parameter such as the toughness at six or more orders of magnitude larger dimensions of scale, I think that Ashby's sobering assessment is an accurate one!
ROR
Toughness is the ability to with stand both plastic and elastic deformation . It is highly desirable quality for structural and machine parts to withstand shock and vibration .
Ductility it is refer to the capacity of substance to undergo deformation under tension without rupture as in wire drawing , tube drawing operation.
To understand the main difference between ductility and toughness, I would recommend studying how material properties are calculated using a stress-strain curve and focusing on how plastic deformation occurs. When a material is elastically deformed, its shape can still return to the original dimensions. However, when it reaches plastic deformation, it can no longer go back to having the original dimensions, before it was pulled. The Elastic Limit link below explains this in detail. Ductility is the ability of a material to deform plastically before fracture. Toughness is the ability of a metal to deform plastically and to absorb energy in the process before fracture.
http://www.admet.com/materials-testing-glossary/#proportional-limit
Greetings,
The area under stress-strain curve indicates the toughness. It involves the strain energy to failure. So can we relate the toughness to impact strength of a material? Does that means materials with high toughness have higher impact strength? But the unit for toughness and impact strength are different.
Thank you.
Hello Ng,
For toughness, like you stated, the sample has to go through constant loading (that is how the stress-strain curve is formed). Impact strength, on the other hand, is when a sudden load is applied to the material. Impact strength can be recorded as energy lost per unit of thickness or energy lost per unit cross-sectional area of the notch. For further information, I would recommend reading about the Charpy and Izod impact testers. Toughness and impact strength should be studied as different material properties mainly due to the very different ways these two properties are measured.
Ng:
The toughness can be measured in many ways, as can the strength. One variable is the strain rate. Accordingly, however you measure the toughness - and you should use a fracture mechanics approach such as measuring quantitative parameters like KIc or JIc rather than the area under the uniaxial strength/strain curve (which merely gives an indication) - you can make the measurements at whatever strain rate you choose. Generally, the impact impact toughness will be related to the toughness measured under quasi-static conditions, but it is generally lower as materials tend to get stronger at higher strain rates which can compromise their ductility and hence toughness.
The same is true for strength measurements - they can be measured at any strain rate. The quasi-static strength and impact strength will likely be related but the impact strength will invariably be higher, due to the rate-dependence of plasticity.
And so in relation to your original question, the (quasi-static) toughness and impact strength are likely to be inversely related.
ROR
Dr. Hou:
The impact toughness, as you may well know, is simply the toughness (or fracture toughness) measured under high strain-rate conditions. As such there is generally a correlation between the toughness measured under quasi-static and impact conditions. However, as high strain rates are often associated with elevations in the flow stress, if these two properties are measured in the same fashion, e.g., in terms of the stress intensity K, then the impact toughness is likely to have a lower magnitude. Moreover, the impact or dynamic fracture toughness is more complex to measure properly as it can be very sensitive to sample size. This is not simply a small-scale yielding or plane strain vs. plane stress issue, but also associated with the propagation of stress waves which can reflect off the sample surfaces. This is the source of so-called Wallner lines which are ripples on the fracture surface of fractured brittle materials, when stress waves emitted by the crack propagate to the sample surface and are reflected back to interact with the growing crack (you can see these on many old cobble stones broken open by cleaving with a hammer).
In simple terms, the bottom line here is simply that the impact toughness is another measure of fracture resistance, only measured specifically under high strain rate conditions.
ROR
As a minor contribution to this thread. In order to perform probabilistic fracture assessments of plant components it is necessary to include correlations between fracture toughness and tensile properties. After all there is no point in having a Monte-Carlo simulation use combinations of properties which are physically impossible (highly unlikely). I was analysing data for thermally aged austenitic stainless steels (wrought, cast and weld; to get a wide range of behaviours) and managed to collate a reasonable set of data (thanks to collaboration amongst the world wide nuclear industry), in which the same material/condition had been tested in (i) fracture toughness, (ii) impact energy and (iii) tensile test. Unfortunately, I never completed the work (as the plant component was plastic collapse dominated and such correlations were not really needed in the end). Nevertheless, I did notice that the (qualitative) correlations between (room temperature, because elevated temperature is a whole new can of worms) properties were:
I should put some statistics to these qualitative observations. Nevertheless, this is a job for later. I am confident ROR can explain these observations, so I won't try.
I do agree with Dr. Robert O Ritchie, just you have to mention which material you mean, where there is difference in mechanical behavior for many materials for example: what about polymeric materials? Means Visco-elastic properties that obey another criteria!
Regards, Emad
Dr. Spindler:
I am fascinated by your description of the difficulties of correlating strength and toughness data and of the use of Charpy samples to somehow obtain meaningful toughness data for real world applications On the latter issue, I looked into the approach of precracking and side-grooving such Charpy samples to be used for nuclear surveillance specimens many years ago, and managed to achieve some success in estimating JIc values in these under-sized samples. My paper is attached.
ROR
I am certainly agree that, in fracture mechanics, stress intensity factor, J-integral, or equivalent values should be used for engineering structural materials, however, for the general assessment of the mechanical properties of materials, the stress-strain curve obtained from simple tensile test gives only a general idea about toughness. (I think it is valuable for traditional steel groups, obtained from tensile test or impact tensile tests developed by ARCELOR (formerly IRSID-FRANCE) It is difficult to say the same idea for the composites, mainly hybrid composite families.
I am sure; Prof. Ritchie can give us more detailed explanation. Thanks a lot for this useful discussion; there are a lot of questions coming from industry or certain academic groups on the toughening mechanism or failure mechanisms on the new materials, composites-hybrid comps, etc.
As a practical matter, ductility as measured in a tensile test (uniform elongation, total elongation, reduction in area, area under the stress-strain curve), as a measure of the ability to plastically deform without failure, has no application to engineering design of components unless one is considering off-nominal ductile overloads of crane hooks, tie rods, etc. One does not design components to operate above yield under normal operating conditions.
On the other hand, fracture toughness is an important measure of a properly designed component's ability to avoid fracture when defects are present. Defects are hard to avoid entirely during component manufacture and installation. Moreover, corrosive environmental conditions and fatigue loads under which the component operates may introduce crack-like defects later in life. When defects are detected, remaining useful life assessments require fracture toughness and crack mechanics. Tensile ductility is of no use. Note, however, that tensile yield stress is the one measure obtained from the tensile test that is used with fracture toughness to determine fracture resistance (critical flaw size).
Given that every engineering material is accompanied by a spec sheet having RT tensile data and that fracture toughness data are relatively unavailable, it may be tempting to attempt to find a correlation of tensile and fracture toughness data. But if you have the fracture toughness data needed for the correlation, why bother? Use the FT data. And if you have only a correlation derived using data obtained on another material, what makes one think that the correlation is universal? Note that measures of tensile ductility are sensitive functions of strain hardening (uniform strain) and strain rate sensitivity (necking strain) and test details (crosshead displacement rate, stiffness of the load train). Ductile behavior at RT does not necessarily translate to a higher temperature where dynamic strain aging may occur, for example.
All that being said, there is one fracture methodology where a measure of "ductility" enters the fracture assessment. These are the cohesive zone models and methods, the Dugdale-Barrenblatt model being earliest of the kind. This model can be expressed in terms of the J-integral as Jc = dcSy where Jc is the critical applied J value, dc is the critical crack mouth opening displacement and Sy is the yield stress. dc could be considered as a measure of "ductility" that might be approximated as the uniform strain measured in a plane-strain tensile test. If you can run plane strain tensile tests, this may be an interesting correlation to attempt.
This is just a small comment regarding Meryl M. Hall, Jr.'s contribution. While I largely agree with Meryl's answer from the perspective of general engineering design at ambient temperature. There are specialist high temperature applications under which thermal strains can result in stresses that are above yield. Of course good design codes try to limit these thermal stresses. However, sometimes the simplifying assumptions made by design codes neglect some sources of thermal stress and plant failures occur. Experience has shown that failure due to these above yield thermal stresses can be predicted much more accurately using strain analysis and ductility exhaustion than by using stress based methods.
It is quite interesting to contrast the differences between Design Codes, which usually assume that the components are defect free (and which contain construction and inspection rules to limit any real defects) and Fitness-for-Purpose codes that enable plant operators to consider the real world in which defects can be present.
Dr. Wang:
Another fascinating question! To the first approximation, the fracture toughness KIc and the Charpy V-notch impact energy are both measures of toughness, and thus should be consistent in tracking the toughness of materials. Indeed, several empirical correlations have been established to relate one measure of toughness to the other. Stan Rolfe and John Barsom's text book "Fracture and Fatigue Control in Structures" (2nd ed., Prentice-Hall, 1987) provides an excellent source of these relationships.
However, as you point out in your question, there are factors that can cause these two measures of toughness to become inconsistent. One is clearly strain rate: Charpy measurements are made in impact whereas fracture toughness measurements are not necessarily performed dynamically. This naturally can result in some degree of inconsistency, but nevertheless, as materials with high toughness under impact loading generally also have high toughness quasi-statically, strain rate is seldom the cause of a breakdown in the correlation of these two measures of toughness.
The principal difference in these two measures of toughness, which can sometimes cause a distinct lack of correlation, is the nature of the stress concentrators: Charpy tests employ a blunt V-notch with a root radius of ~250 microns whereas fracture toughness test samples (should) contain an atomically-sharp (e.g., fatigue) crack. This can cause large differences in what these two measures of toughness can tell you, particularly where you are dealing with course, inhomogeneous, structures. I worked on a particularly good example of this years ago with NiCrMo quenched and tempered steels (AISI 4340), where if you raised the austensitizing temperature from 870C to 1200C (prior to standard quench and tempering), the toughness measured by KIc went up, whereas the Charpy energy went down (see attached file). Wierd right? However, this is caused by a relatively complex interplay between the critical stress (or strain) for fracture and the distance (actually volume) over which this stress must act ahead of the crack tip. In the case of the 4340 steel, large prior austenite grain sizes can reduce the critical fracture stress, which leads to the reduction in Charpy energy, but in the KIc test it also dramatically increases the distance over which this critical fracture stress has to be exceeded at the crack tip, which overrides the lower stress effect and leads to an increase in toughness.
The underlying reason for all this is that that for a stress-controlled fracture, the peak stress ahead of a stress concentrator is roughly two crack-tip opening displacements (CTODs) ahead of a sharp crack, whereas it is roughly at the elastic -plastic interface, i.e., one plastic zone size ry, ahead of a blunt notch. These two distances are vastly different. In terms of the yield stress sy and Young's modulus E, the CTOD scales with KIc2/syE, whereas ry scales with KIc2/sy2. As E is typically 1000 times larger than sy, there is typically three orders of magnitude difference between where the maximum stress peaks ahead of a sharp crack vs. a blunt notch. Since the volume scales with the cube of distance, the volume of material ahead of a blunt notch that experiences these peak stresses (the so-called statistical sampling volume) can be up to 9 orders of magnitude larger than that sampled ahead of a sharp crack, although the magnitude of these peak stresses ahead of the notch will be lower than that ahead of a sharp crack. This is an often unappreciated fact but it is precisely this statistical sampling effect that can cause can a major difference in the ranking provided by these two measures of toughness: the KIc test develops the highest local stresses and thus can cause fracture of, for example, the smallest, most numerous particles, but because of its very small sampling volume compared to a blunt notch test, it may not even see the larger, less numerous, particles. More information of this phenomenon can be seen the second attached paper of mine, taken from the 1978 ASM Conference Proceedings on "What Does the Charpy Test Really Tell Us?" (Incidentally, both these publications are on ResearchGate).
So there's the rub - for highly inhomogeneous materials, the Charpy V-notch toughness test may provide a better assessment of the toughness because it samples a far large volume of the material. However, practically speaking, as notches in real structures invariably sharpen by fatigue in service, most people, and I include myself here, regard the sharp crack KIc test as a more meaningful measure of the fracture toughness as it can be readily applied to predict the behavior of real structures in actual service applications.
ROR
Article Evaluation of Toughness in AISI 4340 Alloy Steel, Austenitiz...
Conference Paper On the Relationship between Fracture Toughness and Charpy V-...
Dr. Hou:
The term "apparent fracture toughness" has been used since the 1970s to describe the fracture toughness value measured ahead of a blunt notch, instead of a sharp crack toughness. The term apparent fracture toughness is presumably used because the calculation is done assuming that a sharp crack was present, not a rounded notch. Since there is a singularity ahead of an infinitely sharp crack, which does not exist ahead of a blunt notch, to the purist its actual numerical value in fracture mechanics terms is effectively meaningless.
However, researchers, including myself, have used this parameter to measure the toughness ahead of notches of various root radii where the variation in apparent toughness with the square root of the notch root radius can provide some mechanistic insight into the fracture mechanisms. Most recently, this approach has been used for bulk-metallic glasses, where the effect of the notch root radius on the apparent toughness is far more extreme than in conventional crystalline materials as the acuity of the notch has a strong effect on the intensity of shear-band formation.
Can such data, i.e., the apparent fracture toughness as a function of the notch root radius, be used to estimate the actual (sharp-crack) fracture toughness KIc. Well in principle yes, as one can extrapolate the toughness data to a root radius approaching zero which ought to give to the KIc value. However, this procedure is fraught with difficulties as the toughness data vs. root radius may not be linear, and more importantly a microstrucurally-relevant limiting root radius is generally observed, below which the toughness doesn't change - this would be presumed to be the KIc value. If you cannot collect data over an appropriate range of root radii, at least though you would now that any value of the apparent fracture toughness will be greater than or equal to the real KIc value.
Accordingly, apparent fracture toughness values have some utility in estimating the true KIc fracture toughness value, particularly in materials than are difficult to fatigue pre-crack, such as ceramics or very brittle metallic alloys, but in isolation, the actual numerical value of an apparent fracture toughness is not very meaningful.
ROR
Dear sir Robert O Ritchie..
when fracture toughness is constant we can select one value as a critical fracture toughness but when become fracture toughness is temperature dependent like in case of tungsten, then can we take one value of critical fracture toughness in a wide range of temperature ?
Thanks
Dr. Shahid:
The fracture toughness is temperature-dependent in most materials, particularly bcc metals. As such, you clearly need to use the fracture toughness value pertaining to the temperature of relevance for your application, whatever that is.
If you insist in the need to use a single value of the toughness for a wide range of temperatures, then you should use the lower-bound of the variation in measured fracture toughness values over that temperature range.
ROR
Dear professor Ritchie:
In some situations, why the material require σs /σb ratio lower than certain value? it seems σs /σb ratio is another toughness or ductility indicator.
the ductility and toughness are contradictory in a few situations, for example ,the very fine grain steel. In this contradictory situation, which one we choose firstly?
Dr. Hou:
The ratio of the yield strength to the tensile strength as a measure of toughness or ductility is a new one to me, and at best would be a highly imprecise indicator of ........... well ......... maybe the degree of strain hardening, which could correlate to ductility as strain hardening can act to delay necking. This in many materials would correlate to an increase in toughness, but not always. Whereas high strain hardening is good for toughness when the fracture mode is strain-controlled, such as when fracture occurs by microvoid coalescence, it can be very bad for toughness when fracture is stress-controlled, e.g., by transgranular cleavage or in many cases of intergranular cracking, as it can lead to much higher crack-tip stresses.
So the ratio of the yield strength to the tensile strength may be a good "rule of thumb" in certain classes of materials to correlate to certain mechanical properties such as ductility or toughness, I wouldn't rely on it for the broad base of materials.
ROR
Dear Dr. Robert O Ritchie,
I was reading your paper about intrinsic toughening and extrinsic toughening ( Ritchie R.O. Mechanisms of fatigue-crack propagation in ductile and brittle solids. International Journal of Fracture, 1999, 100: 55-83. ). In my current understanding, there have several methods (plastic deformation, grain refinement, addition of second particles, alloying elements or fiber) to toughening brittle material. I think that addition of fiber belongs to extrinsic toughening mechanism, while alloying would belong to intrinsic toughening mechanism. But, what about the other methods?
Further, I would like to ask you what is intrinsic brittleness?
Thanks in advanced and best regards,
Xiaoyue
Xiaoyue:
As you point out, intrinsic toughening is invariably associated with plasticity, so that changing the alloy composition, the particulate size and spacing, the particulate/matrix interface, the dislocation mobility, the ease of twinning, and so forth, can all act to promote resistance to fracture in the process zone ahead of a crack tip - this is intrinsic toughening, which is created at nano- to micro-scale length-scales and is most effective in ductile materials.
In truly brittle materials, the sole means of toughening is generally extrinsic toughening, which acts at, or more generally behind, the crack tip to create crack-tip shielding so that the crack locally sees less of the applied forces. This is generally created at coarser length-scales than intrinsic toughening and can occur due to a local phase transformation, such as transformation toughening in zirconia ceramics where the change in crystal structure at the crack tip involves a volume change which is then constrained by the surrounding untransformed material. However, the most ubiquitous mechanisms of extrinsic toughening are crack deflection, where the crack trajectory is made to deviate from the path of maximum crack-driving force, and more importantly crack bridging, where entities such as reinforcement fibers, ductile phases, interlocking grains, uncracked ligaments, etc, bridge across the crack opening surfaces to locally carry load that would otherwise be used to further advance crack extension. Note that these extrinsic mechanisms have no effect on resistance to crack initiation - they act in the wake of a crack; as such, they can only promote resistance to crack growth and thus serve to promote rising crack resistance-curve behavior. Crack bridging in found in numerous material systems, such as composites, monolithic ceramics, and bone, but is less common in ductile metallic materials.
ROR
Those interested in tensile ductility as a measure of toughness should read the paper by F.A. Nichols, "Plastic instabilities and uniaxial tensile ductilities", Acta Metallurgica, 28 (1980), 663-673. Nichols makes reference to the classical Considere (1885) and Hart (1967) papers on the theory of the tensile test. Nichols' paper will answer your questions regarding the several measures of tensile ductility; total elongation, uniform strain, necking strain and reduction in area. Nichols shows that each of these is dependent on strain hardening and strain rate sensitivity of the tensile flow stress and the method used to conduct the test (constant loading rate, constant strain rate). W.J. Duffin developed comparable instability analyses for groove and patch like defects in multiaxial stress fields. Unfortunately I can't find a reference for this paper.
For the practical engineer, dealing with defected installed components, the question "What is the difference between toughness and ductility ?" implies an interest in potential for component failure by either brittle fracture, KIC, or ductile stress overload SOL.
In both cases, assuming that there is crack-like defect of known size, the engineer wants to know what is the critical flaw size, CFS. In the first case, not having a stress analysis, fracture toughness KIC, taken alone, is of no immediate value. However, an estimate of the CFS can be had if the yield stress is also known. By assuming that the max possible far field stress is the yield stress, the CFS can be estimated. Assuming a surface-penetrating, semi-circular thumbnail-crack, acrit = (b*KIC/Sy)2 where b = 0.63 for the assumed crack configuration. Equations for other crack configurations can be found in handbooks.
To illustrate the case of ductile overload the simplest case is the single edge cracked configuration. In this case acrit/W = 1-Sy/Suts provides a quick estimate of the CFS when Sy and Suts are known. W is the ligament width. Calculation of both CFSs provides an estimate of the smallest CFS and the likely failure mode, brittle fracture or ductile overload.
Toughness is the ability of the material to absorb energy until the fracture and it is measured by the area under the stress strain curve for the material. However, it is a function or combination of strength and ductility.
Ductility is the ability of the material to appear large deformation in the plastic zone and measured by the %E or % Reduction of area.
For example, rubber is more ductile than the steel. However steel is more tough than the rubber.
For example, in many cases we are dealing with either ductile materials such as low carbon steel or cupper, tough materials such as titanium alloys, or brittle materials such as ceramics and glasses. Fig. 2-18 explains the differences in the stress strain curve, which may appear in different materials.
SEE THE ATTACHED
Fig. 2-18
Thank you Dear Hassan. The graph has shown the clear and detail info on the toughness of the materials. It's all about the comparison of the toughness between different materials. That means we need to calculate the area under the curve, so that we can conclude which materials are tougher. As can be seen in graph, medium carbon steel is tougher than high carbon steel. So, it's possible that lower strength but ductile material could be tougher than high strength but brittle material as toughness is the combination of strength and ductility. Thanks.
Dear Dr. Meryl M. Hall, Jr.
You are talking about the fracture toughness not the toughness. There is a big deference between them the fracture toughness is a materials property for any materials have a crack and it measured by the fracture toughness KIC. However the toughness is a materials property for ordinary materials and it is measured by the area under the stress strain curve for the material as shown in above Fig. for my previously answer.
Yes, of course I am talking about fracture toughness, KIC or Jc. Fracture toughness technology has proven to be essential to design and operational reliability of engineered components. "Toughness", defined as area under the stress-strain curve is useful for illustrating the tradeoffs between yield/ultimate stress and strain to fracture; however, I know of no practical, quantitative use of the concept.
Dear Ng ductility is represent the x axis of stress strain curve but toughness represent area under the same curve.
Toughness is related to the area under the stress–strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough
Greetings, Dear Xuan,
First of all, sorry for the late reply. From my understanding, formability implies the ability of the materials to undergo plastic deformation to form into complex shape without failure. On the other hand, plasticity refers to the tendency of the materials to undergo permanent deformation under stress.
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