Non-linear analysis of shallow cracks in smooth and notched plates Part 1: Analytical evaluation

2005 ◽  
Vol 40 (3) ◽  
pp. 237-244 ◽  
Author(s):  
G Härkegärd ◽  
A Wormsen
Keyword(s):  
Large Scale ◽  
Elastic Solid ◽  
Linear Analysis ◽  
Single Edge ◽  
Linear Elastic ◽  
Cracked Plate ◽  
Perfectly Plastic ◽  
Double Edge ◽  
Non Linear ◽  
Scale Yielding

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The proposed equation for estimating J makes use of the linear elastic and the fully plastic solution to interpolate over the entire range from small- to large-scale yielding. The elastic geometry factor is obtained by means of the stress intensity factor. In the fully plastic formulation, the plastic geometry factors are obtained by considering a pure power-hardening solid, which reduces at one limit to an incompressible linear elastic solid, and at the other to a perfectly plastic solid. The solutions are given for three basic configurations: a double-edge-cracked plate under tension and bending; a notched plate under tension with a crack at the root of the notch; a single-edge-cracked plate under bending. Both force control and displacement control are considered. The accuracy of the formulae is assessed using the finite element calculations in Part 2.

Two Parameter J-A Estimation for Weld Centerline Cracks in Welded Single-Edge Cracked Plate Under Tensile Loading

2019 ◽  
Author(s):  
Chuanjie Duan ◽  
Shuhua Zhang
Keyword(s):  
Large Scale ◽  
Tensile Loading ◽  
Small Scale ◽  
Material Strength ◽  
Single Edge ◽  
Weld Width ◽  
Elastic Plastic ◽  
Cracked Plate ◽  
Scale Yielding ◽  
Two Parameter

Abstract This work examines the J–A two-parameter characterization of elastic–plastic crack front fields for weld centerline cracks under tensile loading. Extensive finite element analyses (FEA) have been conducted to obtain solutions of constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for the stress field near the tip of mode-I crack, for modified boundary layer (MBL) model and welded single-edge cracked plate (SECP). Solutions of the constraint parameter A were obtained for the material following the Ramberg-Osgood power law. The crack geometries analyzed include shallow and deep cracks, and remote tension loading levels cover from small-scale to large-scale yielding conditions. The effects of weld material mismatch and weld width on crack tip constraint were considered in the FEA. A constraint parameter AM, only caused by material strength mismatch, is defined and its parametric equation was obtained. The total constraint in the bi-material weldment can be predicted by adding together AM and A in the homogeneous material. Good agreements were achieved for welded SECP specimen with different crack size and weld width from small-scale to large-scale yielding conditions. This methodology would be useful for performing constraint-based elastic-plastic fracture analyses of other welded test specimens.

Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

1976 ◽  
Vol 98 (4) ◽  
pp. 289-295 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Stress ◽  
Large Scale ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Strain ◽  
Linear Elastic ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Crack Problems ◽  
Scale Yielding

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

Comments on “A new procedure for measuring the decohesion energy for thin ductile films on substrates,” by A. Bagchi, G. E. Lucas, Z. Suo, and A. G. Evans [J. Mater. Res. 9, 1734 (1994)]

1996 ◽  
Vol 11 (8) ◽  
pp. 2109-2111 ◽  
Author(s):  
O. Jørgensen ◽  
A. Horsewell ◽  
B. F. Sørensen
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Crack Tip ◽  
Bilayer Film ◽  
Sufficient Condition ◽  
Elastic Analysis ◽  
Tensile Stresses ◽  
Linear Elastic ◽  
Additional Layer ◽  
Scale Yielding

A recently proposed method for measuring decohesion energy of ductile films on substrates is discussed. The loading mechanism that causes the decohesion of the ductile film is that of gradually depositing an additional layer, with large residual tensile stresses, on top of the film. Hence, the method involves the decohesion of a bilayer film on a substrate. The suggested method assumes that the unloading of the film is controlled entirely by elasticity. This assumption is a prerequisite for the suggested linear elastic analysis, from which the interfacial debond energy is derived in closed form. However, as is shown in the present comment, large scale yielding can occur in the wake of the crack tip and is prohibitive to the suggested linear elastic analysis. A sufficient condition for the occurrence of said large scale yielding is outlined in the present comment. Indeed it is shown that large scale plasticity must have occurred in the experiments described by Bagchi et al.1

Constraint Quantification of Single Edge Notched Bend Specimens Under Large-Scale Yielding

2003 ◽  
Author(s):  
Yuh J. Chao ◽  
Xian-Kui Zhu ◽  
Yil Kim ◽  
M. J. Pechersky ◽  
M. J. Morgan ◽  
...  
Keyword(s):  
Large Scale ◽  
Crack Tip ◽  
Bending Moment ◽  
Additional Term ◽  
Small Scale ◽  
Bending Stress ◽  
Single Edge ◽  
Crack Tip Fields ◽  
Scale Yielding ◽  
Crack Tip Constraint

Because crack-tip fields of single edge notched bend (SENB) specimens are significantly affected by the global bending moment under the conditions of large-scale yielding (LSY), the classical crack tip asymptotic solutions fail to describe the crack-tip fields within the crack tip region prone to ductile fracture. As a result, existing theories do not quantify correctly the crack-tip constraint in such specimens under LSY conditions. To solve this problem, the J-A2 three-term solution is modified in this paper by introducing an additional term derived from the global bending moment in the SENB specimens. The J-integral represents the intensity of applied loading, A2 describes the crack-tip constraint level, and the additional term characterizes the effect of the global bending moment on the crack-tip fields of the SENB specimens. The global bending stress is derived from the strength theory of materials, and proportional to the applied bending moment and the inverse of the ligament size. Results show that the global bending stress near the crack tip of SENB specimens is very small compared to the J-A2 three-term solution under small-scale yielding (SSY), but becomes significant under the conditions of LSY or fully plastic deformation. The modified J-A2 solutions match well with the finite element results for the SENB specimens at all deformation levels ranging from SSY to LSY, and therefore can effectively model the effect of the global bending stress on the crack-tip fields. Consequently, the crack-tip constraint of such bending specimens can now be quantified correctly.

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