Quantification of constraint effects in fracture mechanism transition for cracked structures under mixed mode loading

Abstract

A B S T R A C TThe objective of the study is to evaluate the effects of plastic constraint on transition between tensile-type and shear-type fracture . The T-stress is employed as the quantifying parameter for constraint and is incorporated into the existing theoretical criteria for modelling this transition. It is found that different constraint levels can dramatically alter the transition point. To verify this finding, two sets of mixed mode tests with different constraint levels are carried out. Alongside the theoretical and experimental study, finite element simulation is performed to verify and support these findings. Substantially improved agreement is observed with experimental data if the effect of plastic constraint on transition is included. a = crack length r, θ = crack tip coordinates r c = characteristic distance B = biaxiality ratio (dimensionless T-stress) E = elastic modulus F I , F II = mode I and mode II geometry factors F m = function defining the relation between mode I stress intensity factor and parameter m, m being σ θθ , σ rr , σ rθ J = J-integral K I , K II = mode I and II stress intensity factors K Ic = mode I fracture toughness measured from a standard test L, W , t = specimen length, width, thickness M p = mixity parameter P Ic = fracture load of mode I, highly constraint specimen P c = fracture load of mixed mode specimen P tensile c = fracture load of tensile-type fracture predicted employing maximum tensile stress criterion P shear c = fracture load of shear-type fracture predicted employing maximum shear stress criterion T = non-singular term of stress (T-stress) T f = stress triaxiality factor (hydrostatic to von-Mises stress) α = dimensionless characteristic distance σ θθ , σ rr , σ rθ = tangential, radial and shear stress σ y , τ y = tensile and shear yield stressCorrespondence: M. Mostafavi.

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

“…To examine whether or not the stress triaxiality factor T f is a general measure of constraint for ductile material A508, the T f at a characteristic distance of r c = 0.5 mm ahead of the crack tips at J = J IC was calculated and investigated 9,20 . The T f was defined as: where σ m is the hydrostatic stress and is the von Mises equivalent stress.…”

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

“…Later it was found that the description of out‐of‐plane constraint should include an additional parameter such as a body size in the z ‐direction or the specimen thickness. The authors of Refs 1–8 presented description of the thickness effect on crack‐tip constraint on the basis of numerical results. In particular, authors 9,10 stayed that three‐dimensional (3D) constraint effect along the crack front in a thin plate and in thick SENB specimens can be well represented by the J − A 2 solution accounting for the higher‐order terms under both small‐scale yielding and large‐scale yielding conditions.…”

Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion

“…Ayatollahi and his co‐workers modified the SED criterion, also considering the effects of T ‐stress as well as SIFs. The modified fracture criteria mentioned previously can provide better predictions for mixed mode brittle fracture compared with the conventional fracture criteria, which ignore the influence of T ‐stress . The T ‐stress as well as SIFs have been recognized as two significant parameters in brittle or quasi‐brittle fracture …”

“…The modified fracture criteria mentioned previously can provide better predictions for mixed mode brittle fracture compared with the conventional fracture criteria, which ignore the influence of T-stress. [7][8][9][10][12][13][14][15][16][17] The T-stress as well as SIFs have been recognized as two significant parameters in brittle or quasi-brittle fracture. 18,19 In addition to the energy and stress-based criteria, some strain-based criteria have been also put forward during the past few decades.…”