# What is Fracture mechanics: Definition and 16 Discussions

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.
Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip. A number of different parameters have been developed. When the plastic zone at the tip of the crack is small relative to the crack length the stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised using the stress intensity factor

K

{\displaystyle K}
. Although the load on a crack can be arbitrary, in 1957 G. Irwin found any state could be reduced to a combination of three independent stress intensity factors:

Mode I – Opening mode (a tensile stress normal to the plane of the crack),
Mode II – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front), and
Mode III – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front).When the size of the plastic zone at the crack tip is too large, elastic-plastic fracture mechanics can be used with parameters such as the J-integral or the crack tip opening displacement.
The characterising parameter describes the state of the crack tip which can then be related to experimental conditions to ensure similitude. Crack growth occurs when the parameters typically exceed certain critical values. Corrosion may cause a crack to slowly grow when the stress corrosion stress intensity threshold is exceeded. Similarly, small flaws may result in crack growth when subjected to cyclic loading. Known as fatigue, it was found that for long cracks, the rate of growth is largely governed by the range of the stress intensity

Δ
K

{\displaystyle \Delta K}
experienced by the crack due to the applied loading. Fast fracture will occur when the stress intensity exceeds the fracture toughness of the material. The prediction of crack growth is at the heart of the damage tolerance mechanical design discipline.

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1. ### Derivation of Griffith's Criterion

I did my derivation for a beam as shown with Young's Modulus ##E##, width ##w##, crack length ##a##, and surface energy density ##\gamma##. I understand that a crack will propagate when the free energy ##G## decreases with increase crack length ##a##. Free energy is the combination of the...
2. ### Fracture in Switch Rail: Investigating R260 Steel

Hello everybody We saw a fracture in a switch rail, now we're trying to find the reason, may be you can help us. This rail is made of R260 steel. Let me know if any other information is needed. I have attached pictures of this rail. Thanks in advance
3. ### Fracture mechanics, stress intensity, fracture toughness

I've been giving this some thought. It's clear that the stiffners will increase the resistance of the material so that the energy release is no longer high enough to cause further fracture. I'm just not sure what formula I can use to take into account the new resistance. I suspect part 1 of the...
4. ### Fracture Mechanics: Proving Stress Intensity Factor Superposition Principle

I am trying to prove the superposition principle of stress intensity factors (SIFs). The superposition principle states that the stress intensity factors obtained from the boundary loading are equal to those obtained from the crack face traction loading. I used a flat plate model with the size...
5. ### Notched specimen under constant K and temperature gradient

Hello all, It seems like a fairly straightforward question but I cannot find any information in the literature. Let's suppose we apply a crack driving force K1=45 MPa.m^0.5 to a notched specimen with an upper shelf fracture toughness K_mat = 50 MPa.m^0.5 at room temperature T0=20 oC. Under a...
6. ### Modeling fracture flow in stress field in COMSOL

I am new to COMSOL and I want to model fluid flow in stress field. As starting point I want a simple 2D box having a fracture from right to left while pressure gradient vertically. I want to know the threshold value of that pressure from top which allows flow of fluid in fracture. Can anyone...
7. ### Fracture mechanics - understanding required

I had posted this in the General Engineering forum but perhaps it is a better question for mechanical engineering forum: 1) Consider a centre crack specimen subjected to a wedge load a shown in the figure: https://www.physicsforums.com/attachments/centre_crack_wedge_load-jpg.112584/ In such a...
8. ### How to calculate Stress Intensity Factor?

Hello everyone, I am currently doing my masters research project on fracture mechanics. My problem is such that I have a flat circular disc(brittle) which is simply supported around its circumference. The top surface of the disc is subjected to a point load at its centre. the bottom surface has...
9. ### How to determine fracture toughness Kic from a punch test?

I am looking to determine fracture toughness for aluminium, from a punch test. I have the dimensions of the specimen and the load-displacement curve of the test. I have seen how to calculate Kic for brittle materials from a punch test but am struggling to find a formula for ductile materials...
10. ### Fracture Mechanics Problem: Max Slit Length Without Fracture

Hi everyone, I have a problem that I hope someone can help me with, the question is. A mass of 500kg induces a tensile stress in a glass sheet restrained at the top. Given that the fracture strength of sound glass is 170MPa what is the maximum length of slit that can be tolerated without...
11. ### Pump Jack force - fracture mechanics

Hey everyone, Im having some major trouble with an assignment that I just can't figure out what to do with it. we have been given a pump jack similar to below: http://en.wikipedia.org/wiki/File:Pump_Jack_labelled.png Ignore the belt attachment and gearbox, ours just has motor to...
12. ### Where do the units for fracture energy come from in this equation?

I am having trouble understanding where the units to fracture energy come from when worked out with the following equation. 2\gamma_{ef}=\frac{K^{2}_{Ic}}{E} fracture energy = fracture toughness/young modulus i asked my teacher as this is part of my coursework but he was not able to...
13. ### Can ABAQUS accurately predict fatigue life using crack propagation?

I am curious if anyone here is familiar with ABAQUS and using it for crack propagation. I am doing a project on fatigue life and need to use a computer program (ABAQUS is our FEA) to predict fatigue life under specific loading conditions. I am planning to use crack propagation to do this and...
14. ### Fracture mechanics versus Damage mechanics

Hello, I was wondering if someone could clarify the major differences and limitations of Damage Mechanics and Fracture Mechanics. I'm more familiar with the fracture mechanics approach, but have never done any damage mechanics before. I'm just trying to sort out in my head how fracture...
15. ### Fracture Mechanics - Crack Propagation and Stress Intensity Factors

I am trying to determine the critical crack length of a part using finite element analysis. The software I am using (ABAQUS) has the ability to perform fracture analysis. I model the part, create a crack, and ABAQUS will output the stress intensity factors (modes I, II, and III) and contour...
16. ### Short Tutorial on Fracture Mechanics

http://www.shodor.org/~jingersoll/weave4/tutorial/tutorial.html