Dear Sayali,

1. Fracture toughness can be theoretically estimated. Please find enclosed a papers discussing theoretical estimation.

2. There is a relationship between yield strength and fracture toughness which called Griffith's energy criterion: KIC=s(a)^0.5=(Er/pi)^0.5

KIC is the fracture toughness, s critical strength for crack propagation, a the crack length E young modulus (which relates to yield strength) , r surface energy. There is an additional relation to the ultimate tensile strength, which can be found in the attached publication.      

3. As you can see from the above equation there is a direct relationship between E to fracture toughness and therefore for hardness.

Article On the Relationship Between Critical Tensile Stress and Frac...

Thank You so much Ravit.

Dear Sayali:

Actually the relationship between fracture toughness and yield strength depends very much on the fracture mechanism.  As Ravit mentions, for brittle (stress-controlled) cleavage fracture, the toughness is essentially inversely related to the strength, raised to a power which is a function of the strain hardening coefficient.  However, for ductile (strain-controlled) fracture, e.g., by microvoid coalescence, the simple models suggest that the fracture toughness KIc scales with the square root of the yield strength, multiplied by the elastic modulus, ductility and a microstructural length-scale (e.g., which is some multiple of the particle spacing).

These simple models for ductile and brittle fracture are described in the attached paper:

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.

ROR

Dear Sayali,

I am completely agree with the previous answers and I would add that from a practical point of view the toughness of a material could be qualitative predict form the tensile test curve: toughness is the energy under the tension-deformation curve.  Therefore, to induce a notable increase in toughness the best way is trying to induce a strain-controlled fracture mechanism as Robert says.

If you increase yield strength or hardness (rigidity, E)  toughness will be increased, but the effect will not be remarkable, because deformation capability at the same time will be decreased.

Recently we have published how deformation capability has been induced in a fragile polylactide  and a further publication explaining this mechanism will be available in some months.

Article High toughness biodegradable radiopaque composites based on ...

Hi Sayali

I do agree with the above experts. In my opinion;

Fracture toughness of a particular material is the energy absorbed by the material during fracture. In addition , fracture toughness is the estimated area under the stress-strain curve of the tensile test of the material. So to answer your set of questions:

1-It would be better to experimentally determine the fracture toughness of the materials rather than predicting the value.

2- From the stress-strain curve of the tensile test of the material, you can qualitatively relate the yield strength to the fracture toughness(area under the curve). In general, a smaller area under the curve is normally recorded for a brittle material fracture (normal stress -control)than the ductile materials fracture(shear stress-control).

3-

Yes the hardness of a material can affect the fracture toughness. In general, the harder the material the lower the fracture toughness.

4- Yes,

fracture toughness is related to geometry of component. So, there is ASTM standardized sample geometries for determining the fracture toughness of materials.

5- Yes,

the mode of crack (mode I, mode II, mode III) affects the value of fracture toughness, dependent on the ASTM standardized sample geometries.

useful discussion

Dear Ahmed

if you think so, then, Thank you!.

Yield strength is the measure of the stress that a metal can withstand before deforming. Tensile strength is a measure of the maximum stress that a metal can support before starting to fracture. Fracture toughness is a measure of the energy required to fracture a material that contains a crack.

Above discussions are interesting. From the definition, the toughness has an estimated relationship with the proof stress, tensile strength, and elongation as shown in the following link:

https://www.researchgate.net/post/What_are_the_differences_between_Toughness_Fracture_toughness_and_Fatigue_fracture_toughness

Some estimated results:

Research Proposal Toughness estimation based on standard tensile data

I have a question, how do the fracture toughness and yield strength curves if plotted as a function of temperature would change if a sample was irradiated?

Rigoberto:

In answer to your question on the effect of irradiation on yield strength and fracture toughness, if we consider a relevant material such as the nuclear pressure vessel steel which is used for the containment vessel for the nuclear pile, neutron irradiation serves to increase the defect density which invariably leads to irradiation hardening over time; hence it raises the yield strength. However, such irradiation hardening also acts to degrade the fracture toughness. This is especially critical for the upper-shelf toughness (above the ductile-brittle transition), and actually which this upper-shelf toughness becomes too low due to such irradiation embrittlement, this can can lead to the closure of the reactor.

ROR

1. Is there any impirical relation between fracture toughness and yield strength?

Yes.

KIc2 = a * Sy2 / 2.5

2. How can Fracture Toughness be found out if not by experimentation?

Experimentation in necessary

3. Can yield strength relate to fracture toughness?

KIc2 = a * Sy2 / 2.5

4. Does hardness of a material affect the fracture toughness?

Yes.

5. Is Fracture Toughness related to geometry of component?

No. it’s the materials property, not related to geometry, (however different standard specimens gives different values).

6. Also does the mode of crack (mode I, mode II, mode III) affect the value of fracture toughness?

if the material is orthotropic, than value of fracture toughness is differs in all the modes.

Please, consider Dugdale (1960) who investigated the yielding of steel sheets containing slits. Dugdale considers in plane strain a slit along the x1-axis, from −c to c , and loaded under uniform tension along x2; plastic zones extend from the slit tips over short distances. The applied stresses are lower than the yield stress. He obtains a relation between the lengths of the slit and the plastic zone and the applied stress. He shows that it is in good agreement with experimental measurements of lengths of plastic domains ahead of loaded slits in a steel. Modelling further, a dislocation free zone (DFZ) between the crack and the slip dislocations has been included into the analysis (Chang and Ohr, 1981, 1982; for a review see Ohr, 1985). This allows high stresses to be attained at the tip of the crack, a necessary condition for brittle fracture propagation, and common crack tip behaviors (to be stressed in the present study) between isolated cracks and cracks surrounded by physical dislocations. Then a mathematical relation involving stress intensity factor KI, yield stress sigmay and lengths of crack and plastic zones emerges. This is obtained by Chang and Ohr and also by Anongba and Vitek (2003). This is eq.(14) in the later work “Significance of the deviations of the crack front into the plane perpendicular to the crack propagation direction I. Crack-front dislocation generation” International Journal of Fracture 124: 1–15, 2003.

This gives a linear relation between KI and yield stress sigmay.

Thanks for attention

May be I have to add that we can reach the energy release rate G (or crack extension force) by using the usual plane strain relation; then equating G to twice the surface energy gives the KIc fracture toughness. The assumptions, under which the usual plane strain relation applies, have been stressed by Anongba and Vitek (2003).

Dear Sayali ,

Prof. Robert O Rithchie's reply addressed your question well. Here I only give my supplementary comments.

The fracture toughness is largely dependent on the crack propagation mechanisms. The plastic deformation at the the crack tip contribute a lot on the crack resistance, i.e., the fracture toughness, which usually absorb the energy of the crack. That is why the metals exhibits a higher fracture toughness than ceramics. The radius of the plastic zone is critical. Usually such radius is large for metals (ductile fracture), eg. in mm range, but is very small for ceramics (brittle fracture), e.g., in nm range, closing to the lattice spacing.

Looking back to your question, there is a relationship between the fracture toughness and the Yielding strength through the radius of plastic deformation. Radius of plastic zone=(fracture toughness)^2/(2Pi*yielding strength^2)。 According to this equation, you can think what factor control the plastic zone size, and then you might get answer how the fracture toughness related to the yielding strength, although they have no simple relationship.

Most of fractured surfaces in real materials under general loading are non-planar.

1) Dislocation generation from the crack-front modifies the crack from planar to non-planar (treated to some extent by Anongba and Vitek 2003)

2) Under general loading mixed mode I+II+III, the shearing stresses promote non-planar crack propagation.

The modelling presented above can be readily extended to non-planar crack, please see "Non-planar crack with crack-front plastic yielding under general loading" in our contributions in RG.

Dear Sayali,

Please find in the attached paper different ways to estimated the fracture toughness at nanoscale, which can be used with coarse-grained materials.

Yes, the hardness of a material affect the fracture toughness.

Dear Sayali,

To determine the properties of a material, many software components have been developed (for example, I have established some dependences of properties on the chemical composition of nickel alloys), with their help it is possible to determine or develop dependencies that determine the yield point, toughness or hardness.

What about the filling minerals? I lot 100's km of drill core. Most of the fractures are filled or "cemented", wholly or almost wholly, except for some channels. Is the fracture toughness for unfilled "clean" or cut fractures or walls of those? I would be interested in the effects of toughness and any poroelastic effects of the fracture fills together with fracture walls of host rock. And also relation of toughness or similar measures to porosity of fracture fill or altered rim of walls.

The fracture toughness is in good agreement with the Charpy impact energy. The Charpy impact energy was positively correlated with the toughness which related to the yield point, tensile strength, and elongation in Ref.:

Preprint A simplified toughness estimation method based on standard t...