1.Is the fracture mode cleavage or other brittle mode in small scale yielding or stress lower than yielding situation certainly?
2.Is the fracture strength of steel containing cracks lower than steel have no cracks certainly?
1. Could you please explain more what are you trying to ask.
2. Generally, the fracture strength of steel containing crack will be lower than the steel with no crack. The stress intensity factor will play a role and will generate fracture at lower stress for steels with cracks.
Dr. Hou, to answer your questions:
1. The answer to your first question depends somewhat on how you describe the term "brittle". My doctoral supervisor, Dr. John Knott, used to describe brittle fracture in real materials as fracture, which on the scale of observation, has limited plasticity involved. It is not a well defined term though, except for ideally brittle materials which fail by breaking an atomic bond cohesively at the crack tip, as opposed to a ductile material which fails by first emitting a dislocation. This is a clean definition but real materials invariably always show some degree of plasticity (or more broadly inelasticity) prior to fracture. So for such real materials in general, we can say that small-scale yielding conditions will mean that there is less plasticity involved in the fracture process, which will certainly favor a more "brittle" mode of fracture such as cleavage. However, fracture under small-scale yielding conditions does not mean that the fracture cannot take place by a locally ductile mode, such as microvoid coalescence. Face-centered cubic metals such as aluminum, do not show a ductile-brittle transition and fail with limited plasticity at low temperatures by what is regarded as a "ductile mode" (microvoid coalescence), yet these failures are often in small-scale yielding. The bottom line is that if you can make your specimen large enough so that the plastic zone is less than roughly an order of magnitude smaller than the in-plane dimensions of crack size and the size of the uncracked ligament, your specimen will be in small-scale yielding regardless of the failure mode, which will depend on the material, microstructure and temperature, etc. So small-scale yielding will not guarantee a brittle fracture mode although the extent of plasticity must be small, specifically compared to the in-plane dimensions of your component or specimen..
2. The fracture strength will clearly depend upon the presence of defects, specifically their size, shape, location, etc. This is what the Griffith criterion is all about (the strength is inversely proportional to the square root of the crack size) and is embedded in modern fracture mechanics with a characterizing parameter such as the stress intensity factor which depends not simply on a stress but also is a function of the crack size. Will the fracture strength of steel then be lower when it contains a crack compared to the same steel with no crack? Well, provided the location of the crack is damaging, of course it will - however, you will never be able to find a piece of steel, or any other engineering material for that matter, that contains no cracks (unless perhaps if it is vanishingly small in size). All engineering materials contain cracks - it's not whether they are there or not - they're always there - it's how large they are that it important in governing the fracture strength. Ask any ceramist - they know this only too well!
Dr. Robert :
1. What’s the meaning of Fast Fracture? Could it be microvoid coalescence fracture? Could it be microvoid coalescence fracture when fracture stress is lower than yiled stress?
2.Why people are pursuing and researching high or ultrahigh strength steel in aerospace and automobile industry ,rather than say high or ultrahigh toughness steel if high toughness is more resistant to fracture?
It’s lucky to receive answers from world well-known scientist .appreciate your answering always.
Prof. Ricthie,
As you explained nicely about the ductile and brittle fracture, could you elaborate a bit more on SSY condition. Is it the condition where plastic zone is much smaller in comparison to specimen dimensions? (how samller).
or is it the condition where stresses are self similar along the thickness ?
or is it the condition when T stress = 0?
All of above might happen simultaneously but which is the necessary and sufficient condition?
Dr. Hou:
1. "Fast fracture" is a relatively imprecise term but it generally means final overload fracture which is generally catastrophic in nature. It does not exclude, but is less likely to involve, a microvoid coalescence failure, but it could. Such a microvoid coalescence fracture would be highly unlikely to occur at a fracture stress less than the yield strength (but this can be only an approximate comparison because the yield strength is defined as a global stress to cause yielding in typically an unnotched uniaxial tensile test, whereas the fracture stress can be measured in many ways is more likely to be motivated locally by an imperfection or stress concentration).
2. This is a good question, although there is no precise answer, In the aerospace and nuclear industries, the relevance of high toughness is well appreciated, but in general engineering, the value of high strength is often the first property to be considered (as smaller section sizes can be used, which can save weight, etc.). Fracture mechanics is not always used in general engineeing, as compared to conventional mechanics, it is a relatively young field (just over 60 years old). Once a steel, or whatever material, is selected for an application requiring high strength, the next consideration is invariably the tensile ductility, as this is the "safety valve" for the designer, i.e., the material will not fracture catastrophically without warning - one can never underestimate this in engineering design. More industries now though are considering the toughness as well, and so things are slowly changing. What is interesting though is that many materials are still selected for a given application on the basis of strength, yet the properties that ultimately are life-limiting are more likely to be the toughness and particularly the fatigue resistance. But as I stated above, things are changing and it is increasing evident that the life-limiting phenomena, be it overload fracture, fatigue, stress corrosion, whatever, are now being more actively considered up front before a material is selected for a given application. In that respect, I think that the "Ashby maps" have been incredibly useful in this regard as they provide the designer with a scientifically rational basis to select materials for a given application in terms of numerous combinations of mechanical and physical properties.
Dr. Tiwari:
The state of "small-scale yielding" is the requirement that the extent of local plasticity is small enough to ignore so that linear elastic fracture mechanics (LEFM), i.e., K-field crack-tip dominance, can be assumed. As the K-1/r1/2 singular field is a planar field, this specifically means that the plastic zone size ry must be small (typically an order of magnitude or so smaller) compared to the in-plane specimen (or component) dimensions of crack size a and uncracked ligament size b. In the ASTM E399 fracture toughness standard, this is written as a, b > 2.5 (K/Y)2 where K is the stress intensity and Y is the yield strength. Without this condition being met, K is essentially useless in characterizing the crack tip field and one needs to turn to alternative methodologies such as nonlinear elastic fracture mechanics. However, it says absolutely nothing about the out-of-plane stresses. This is a separate criterion involving the out-of-plane thickness B being large compared to the plastic zone size, which sets the condition of plane strain. Thus to measure the plane-strain fracture toughness KIc, to achieve a "valid" number in terms of ASTM LEFM standards, you need to satisfy two separate criteria: (i) the condition of small-scale yielding (ry
Dr.Robert :
Does it mean the global stress is lower than global yield stress, when satisfy small-scale yielding ? If so, in KIC testing of hig toughness metal , which satisfy the two separate criteria, the fracture happen when global stress is lower than global yield stress. will the fracture mode be microvoid coalescence?
Dr. Hou:
Actually unlike the yield strength, the fracture stress in a uniaxial tensile test is not that useful a parameter and so it is difficult to compare these global stresses. Suffice to say, there is no such thing as "purely elastic fracture" in metallic engineering materials and so the local fracture stress that controls the fracture event will almost certainly be higher than the initial yield strength. In structural steels, for example, the sequence of local events is often a dislocation pile-up at a carbide particle (or occasionally an inclusion) which must occur at stresses at or above yield stress, the formation of a crack in that particle (which in low carbon steels will generally be at a grain boundary), the exit of the crack in the particle into the (ferrite) grain, and then the propagation of that running crack in the grain through the next grain boundary. Depending upon the temperature, one of these processes will be the rate-limiting step for cleavage fracture, but they all occur at a stress (the highest of which will constitute the fracture stress) that must exceed the yield strength.
However, as the test temperature is raised, the yield strength of the steel will decrease, and eventually there will be will not be enough local stress developed ahead of a crack (which scales with the yield or flow strength) to exceed this local fracture strength (which is relatively less dependent on temperature). The material strain hardens in an attempt to raise this crack-tip stress but eventually a critical strain will be exceeded for the development of microvoid coalescence. This essentially constitutes the brittle-to-ductile transition in a real material, such as a structural steel, i.e., it is the temperature where the elevation of the flow stress at the tip of a crack is insufficient to exceed the local fracture strength to cause cleavage or some other mode of nominally brittle fracture.
If you're interested, this is quite well explained in the opening paragraphs 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),1987, 641-51.
ROR
Prof. Ritchie,
As you mentioned that inclusions or carbides fail at stresses which are locally higher than yield stress preceded by dislocation pile up, is it true that even at high temperature the carbides or inclusion will fail from within and not debond from interface?
Generally, most of the inclusions are brittle as carbides are so in what case the interface of the secondary face and matrix will play important role?
Will the inclusion/carbide always fail and debonding of interface will never occur? if that is so, is there any importance of Argon's and Beremin's stress criteria on MnS inclusions?
When you say "The material strain hardens in an attempt to raise this crack-tip stress but eventually a critical strain will be exceeded for the development of microvoid coalescence." --- do you mean that voids would already have nucleated before this critical plastic strain criteria is fulfilled? if that is so why not a debonding occured at the interface due to strain difference in the inclusion and matrix?
Dr. Tiwari:
All the early notched-bar work by Cotterell, Knott, Smith, and later statistical studies by Evans and myself (and others), indicated that at the lower temperatures in many ferritic steels, where the yield strength is high, the the stress to cause a dislocation pile-up at a particle will be close to the fracture stress; in this regime, fracture is nucleation-controlled (the generation of a crack in the particle) and the local fracture strength can be equated to the flow stress. As one increases the temperature though (but still in the lower shelf region), other rate-determining steps become dominant and fracture generally becomes growth-controlled, specifically because the stress to get the crack out of the particle into the matrix grains (i.e., the fracture strength of the particle) will become higher than the diminishing yield strength. However, at higher temperatures still, the stress to get the crack through the matrix grain and through the next grain boundary becomes dominant - this is because the local event is a dynamic one and this crack has to carry with it its plastic zone formed in the weaker matrix and which gets larger as the matrix yield strength becomes lower. In gory detail, you're correct - all these events will depend upon the specific nature of the particle and the nature of the interface, etc.; in steels carbides invariably crack whereas inclusions are more likely to debond. Eventually, as I mentioned before, there simply isn't enough work hardening to elevate the flow stress at the crack tip to exceed any of these stresses - as such, stress-controlled ("brittle") fracture can no longer occur as it is easier to exceed a strain-controlled ("ductile") fracture criterion, e.g., for microvoid coalescence. I'm not sure if one can define a general critical step for all materials in this instance, but it is certainly related to the coalescence of some number of pre-existing voids that have formed around particles. So the voids created at debonding or cracked particles would definitely exist prior to actual microvoid coalescence fracture; fracture ensues by the coalescence of these voids, either by their impingement or more likely by strain localization between them - this would be the most likely process for the critical strain for such "ductile" fracture (which incidentally is also markedly affected by the stress-state).
ROR
Dear Robert :
some questions consult you again .
1.What’s the function of plastic zone at crack tip in retarding crack propagation? Is it because the plastic zone blunt crack tip,then mitigate stress concentration?
And in the calculation of stress and strain distribution ahead of crack tip ,it seems not include the influence of blunting.(e.g σ_xx=K_Ⅰ/√2ar (1-sin ( θ)/2 sin 3θ/2) ,K_Ⅰ=σ√(πa ) )
2. In transgranular cleavage fracture, if the critical step is propagation, once crack nucleate ,it will stop propagation and blunt .Will the blunted crack propagate?
3.What’s qusi-cleavage fracture mechanism? There are many literatures about qusi-cleavage, however few about the mechanism.
Prof Ritchie,
To your answer further
If I think of a reference unit volume where a carbide is located and it cracked at its failure stress in a relatively ductile matrix where plastic strain increased to promote microvoid coalescence as you mentioned. Due to these micro-voids acting as penny shaped cracks individually the local stresses around it should increase by at least a factor of 3. As micro-voids will be surrounding the failed carbide the stress around it has increased. Do you think for a very small difference of plastic strain failure criteria n micro-crack dynamic propagation criteria the initial micro crack which was not able to propagate can now propagate due to increased stresses around it by voids ? Of course the stress amplification will be truncated by YS; but for a marginal difference in strain based n stress based criteria to be met , where work gardening can help reach to that stess, will it be possible?
What would be the case of If I increase the constraint of this reference volume?
Dr. Hou:
1. The plastic zone does exactly that - it blunts the crack tip and with the energy used to move dislocations within this region, the role of plasticity is very much to toughen the material, acting as the prime intrinsic toughening mechanism to inhibit both crack initiation and crack growth. It is not accounted for in the crack-tip stress and strain distribution that you cite because you have written the linear-elastic stress and strain singularity (Williams') solution for the crack-tip fields (i.e., for K-dominance at the crack tip). If you want to account for plasticity (or more correctly nonlinear elasticity), you need to refer to the equivalent nonlinear-elastic crack-tip singular fields, which is known as the HRR (Hutchinson, Rice, Rosengren) singularity, which is the basis of J-field dominance at a crack tip.
2. Will blunting stop crack propagation, Well, it depends on the degree of blunting. All cracks in real metallic materials possess a plastic zone at their crack tip, whether they are stationary or propagating, and so are not atomically sharp, i.e., they have some degree of blunting. Whether the nominally brittle crack arrests or not though depends on a multiple of factors, such as the nature of the loading, including the compliance of your testing system, local microstructure, excessive crack-tip blunting, and so forth.
3. Quasi-cleavage is a vague and often misused term to describe "brittle-like" fracture surfaces that don't look exactly like the classical brittle ones of transgranular cleavage and intergranular cracking. Such a fracture mode is often seen in quenched and tempered steels where the underlying martensitic or bainitic microstructures can distort (for want of a better word) the nature of a nominally transgranular cleavage fracture. Unlike lower strength ferritic steels where the cleavage facets are clean and shiny, and display river marking radiating out from generally a cracked particle on the grain boundary, quasi-cleavage fracture surfaces in martensitic/bainite steels are transgranular yet look more distorted with less distinct facets, often initiated by particles inside the grains rather than at the boundaries, and sometimes with segments of ductile fracture linking the individual (quasi-cleavage) facets. The mechanism has not been explicitly modeled, as far as I know, but it would appear to be similar to that for classical transgranular cleavage, only with a ductile component associated with the linking the facets. This is what I understand by quasi-cleavage fracture. However, as I note above, the term has often been used to describe any fracture mode that doesn't look like one of the classical fracture morphologies!
ROR
Dear Dr. Tiwari:
I'm sorry but I'm a little unsure of what you're asking here but I think that you may be referring to the local fracture criteria that set the elemental probability of failure of a unit volume in statistical models of cleavage fracture, such as the one presented by Lin et al. (1986, 87). To have a critical stress or stress-state modified critical strain criterion that can be statistically handled, the mechanistic nature of the critical fracture event is often necessarily simplistic and so I think you're possibly reading too much detail into exactly what the precise mechanisms may be. Can more advanced models be generated? Hopefully yes, but unfortunately in the U.S., steel research is largely unfunded and at best is extremely limited such that further insight to elucidate the precise mechanistic aspects of the ductile-brittle transition in these materials is unlikely to be forthcoming, at least in this country. Maybe you can pick up the challenge and further our understanding on this issue.
ROR
Prof Ritchie,
Thank you very much for all your answers. Its a privilege and honor to have detailed answers so clear from such a great experienced expert of the subject.
Many thanks.
Abhishek
https://www.researchgate.net/publication/301348952_Licensed_Under_Creative_Commons_Attribution_CC_BY_Investigation_on_Mode_-_I_Fracture_Parameters_Using_Steel_Fibers_in_High_Strength_Concrete
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