the length of the plastic zone is such that the stress intensity factor due to remote tension cancels with crack closure.ġ0 Strip Yield Method SIF due to crack closure stress can be estimated by considering a normal force P applied to the crack at a distance x from the center line of crack SIF for two crack tips are given byġ2 Comparison of plastic corrections with LEFM Concept: stress at the crack tip is no more a singular and it is a finite value (sys), hence stress singularity term is zero. Approximate elasto-plastic behavior is obtained by superimposing two elastic solutions (a) a through crack under remote tension (b) a through crack under crack closure stress. The strip yield plastic zone assumes a crack length of 2a + 2r Where r is length of plastic zone. They assumed a narrow long slender plastic zone ahead of crack tip in a non-hardening (ideal plastic) material in plane stress for a through crack in a infinite plate. If the plate is made of titanium Ti-6AL-4V,(KIC=115 MPa-m1/2, sys=p10 MPa) what is the factor of safety against crack growth for a crack of length a = 20 mm.ĩ Strip Yield Method (Proposed by Dugdale and Barrenblatt) orĦ To permit redistribution of stresses, the areas A and B must be the sameħ A long rectangular plate has a width of 100 mm, thickness of 5 mm and an axial load of 50 kN. Let the effective crack size be aeff, such that aeff = a+d, where d is the correction. Irwin proposed that plasticity makes the crack behave as if it were larger than actual physical size. This is possible if the material immediately ahead of plastic zone carries more stress. The cross hatched regions represents forces active in the elastic analysis that cannot be carried in elasto-plastic analysis, because of the reason that the stresses cannot exceed sys.To redistribute this excessive force, the plastic zone size must increase.
Irwin’s Approach When yielding occurs, stresses redistribute in order to satisfy equilibrium conditions.
This is approximate estimate, because of the fact that syy is based on elastic analysisĥ Let the effective crack size be aeff, such that aeff = a+d, Irwin’s Approach Normal stress syy based on elastic analysis is given by On the crack plane q = 0 As a first approximation yielding occurs when syy = sys ry = first order estimate of plastic zone size. For extensively yielding metals, alternative fracture parameters like CTOD, J-integral are to be used taking into account material non-linearity. For moderately yielding metals, LEFM solutions can be used with simple correction. A small region around the crack tip yields leading to a small plastic zone around it. For metals with yielding, LEFM solutions are not accurate. In addition, inelastic deformations due to plasticity in metals, crazing in polymers leads to further relaxation of stresses. But in real materials, the crack tip radius is finite and hence the crack tip stresses are also finite. For example, two normal stress in x direction caused by two different external load can be added to get total stressįor example consider a plate having semicircular crack subjected to an internal pressureģ Crack Tip Plasticity LEFM assumes a sharp crack tip, inducing infinite stress at the crack tip. For a linear elastic system, the individual components of stress, strain, displacement are additive.
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