Fracture mechanics
The characterising parameter describes the state of the crack tip which can then be related to experimental conditions to ensure similitude.
Known as fatigue, it was found that for long cracks, the rate of growth is largely governed by the range of the stress intensity
gives excellent agreement of Griffith's predicted fracture stress with experimental results for glass.
For the simple case of a thin rectangular plate with a crack perpendicular to the load, the energy release rate,
For materials highly deformed before crack propagation, the linear elastic fracture mechanics formulation is no longer applicable and an adapted model is necessary to describe the stress and displacement field close to crack tip, such as on fracture of soft materials.
The reasons for this appear to be (a) in the actual structural materials the level of energy needed to cause fracture is orders of magnitude higher than the corresponding surface energy, and (b) in structural materials there are always some inelastic deformations around the crack front that would make the assumption of linear elastic medium with infinite stresses at the crack tip highly unrealistic.
[6] Griffith's theory provides excellent agreement with experimental data for brittle materials such as glass.
Naval Research Laboratory (NRL) during World War II realized that plasticity must play a significant role in the fracture of ductile materials.
The plastic loading and unloading cycle near the crack tip leads to the dissipation of energy as heat.
Hence, a dissipative term has to be added to the energy balance relation devised by Griffith for brittle materials.
Another significant achievement of Irwin and his colleagues was to find a method of calculating the amount of energy available for fracture in terms of the asymptotic stress and displacement fields around a crack front in a linear elastic solid.
Next, Irwin adopted the additional assumption that the size and shape of the energy dissipation zone remains approximately constant during brittle fracture.
This assumption suggests that the energy needed to create a unit fracture surface is a constant that depends only on the material.
Today, it is the critical stress intensity factor KIc, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics.
For this reason, in numerical studies in the field of fracture mechanics, it is often appropriate to represent cracks as round tipped notches, with a geometry dependent region of stress concentration replacing the crack-tip singularity.
This deformation depends primarily on the applied stress in the applicable direction (in most cases, this is the y-direction of a regular Cartesian coordinate system), the crack length, and the geometry of the specimen.
In the event of an overload or excursion, this model changes slightly to accommodate the sudden increase in stress from that which the material previously experienced.
This process further toughens and prolongs the life of the material because the new plastic zone is larger than what it would be under the usual stress conditions.
[12] But a problem arose for the NRL researchers because naval materials, e.g., ship-plate steel, are not perfectly elastic but undergo significant plastic deformation at the tip of a crack.
Most engineering materials show some nonlinear elastic and inelastic behavior under operating conditions that involve large loads.
This parameter was determined by Wells during the studies of structural steels, which due to the high toughness could not be characterized with the linear elastic fracture mechanics model.
This curve acknowledges the fact that the resistance to fracture increases with growing crack size in elastic-plastic materials.
The main reasons appear to be that the R-curve depends on the geometry of the specimen and the crack driving force may be difficult to calculate.
[6] In the mid-1960s James R. Rice (then at Brown University) and G. P. Cherepanov independently developed a new toughness measure to describe the case where there is sufficient crack-tip deformation that the part no longer obeys the linear-elastic approximation.
[13] This analysis is limited to situations where plastic deformation at the crack tip does not extend to the furthest edge of the loaded part.
A simple technique that is easily incorporated into numerical calculations is the cohesive zone model method which is based on concepts proposed independently by Barenblatt[14] and Dugdale[15] in the early 1960s.
Bažant (1983) proposed a crack band model for materials like concrete whose homogeneous nature changes randomly over a certain range.
[17] He also observed that in plain concrete, the size effect has a strong influence on the critical stress intensity factor,[19] and proposed the relation
It integrates concepts from fracture mechanics with atomistic simulations to understand how cracks initiate, propagate, and interact with the microstructure of materials.
By using techniques like Molecular Dynamics (MD) simulations, AFM can provide insights into the fundamental mechanisms of crack formation and growth, the role of atomic bonds, and the influence of material defects and impurities on fracture behavior.
