Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part III—Large-Scale Yielding

1991 ◽  
Vol 58 (2) ◽  
pp. 450-463 ◽  
Author(s):  
C. F. Shih ◽  
R. J. Asaro ◽  
N. P. O’Dowd
Keyword(s):  
Large Scale ◽  
Crack Tip ◽  
Field Analysis ◽  
Small Scale ◽  
Homogeneous Material ◽  
Full Account ◽  
Full Field ◽  
Bimaterial Interfaces ◽  
Homogeneous Materials ◽  
Scale Yielding

In Parts I and II, the structure of small-scale yielding fields of interface cracks were described in the context of small strain plasticity and J2 deformation theory. These fields are members of a family parameterized by the plastic phase angle ξ which also determines the shape or phase of the plastic zone. Through full-field analysis, we showed the resemblance between the plane-strain interface crack-tip fields and mixed-mode HRR fields in homogeneous material. This connection was exploited, to the extent possible, inasmuch as the interface fields do not appear to have a separable form. The present investigation is focused on “opening” dominated load states (| ξ | ≤ π/6) and the scope is broadened to include finite ligament plasticity and finite deformation effects on near-tip fields. We adopt a geometrically rigorous formulation of J2 flow theory taking full account of crack-tip blunting. Our results reveal several surprising effects, that have important implications for fracture, associated with finite ligament plasticity and finite strains. For one thing the fields that develop near bimaterial interfaces are more intense than those in homogeneous material when compared at the same value of J or remote load. For example, the plastic zones, plastic strains, and the crack-tip openings, δt, that evolve near bimaterial interfaces are considerably larger than those that develop in homogeneous materials. The stresses within the finite strain zone are also higher. In addition, a localized zone of high hydrostatic stresses develops near the crack tip but then expands rapidly within the weaker material as the plasticity spreads across the ligament. These stresses can be as much as 30 percent higher than those in homogeneous materials. Thus, the weaker material is subjected to large stresses as well as strains—states which promote ductile fracture processes. At the same time, the accompanying high interfacial stresses can promote interfacial fracture.

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.

Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part II—Structure of Small-Scale Yielding Fields

1989 ◽  
Vol 56 (4) ◽  
pp. 763-779 ◽  
Author(s):  
C. F. Shih ◽  
R. J. Asaro
Keyword(s):  
Plastic Zone ◽  
Crack Tip ◽  
Mathematical Structure ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Crack Face ◽  
Crack Tip Fields ◽  
Bimaterial Interfaces ◽  
Scale Yielding ◽  
Crack Face Contact

In Part I we found that although the near tip fields of cracks on bimaterial interfaces do not have a separable form of the HRR type, they appear to be nearly separable in an annular zone within the plastic zone. Furthermore, the fields bear strong similarities to mixed mode HRR fields for homogeneous medium. Based on our numerical results, we have been able to identify a clear mathematical structure. We found that the small-scale yielding crack tip fields are members of a family parameterized by a near tip phase angle ξ, and that the fields nearly scale with the value of the J-integral. In Part II, the original derivation of the mathematical structure of the small-scale yielding fields is elaborated upon. The issue of crack face contact is addressed and the phenomenology is described in terms of the phase parameter ξ. Crack tip plastic deformation results in an open crack for a range of ξ which is nearly symmetric about the state corresponding to pure remote tension. Plane-strain plastic zones and crack tip fields for the complete range of ξ are presented. Over distances comparable to the size of the dominant plastic zone, the stress levels that can be achieved are limited by the yield stress of the weaker (lower yield strength) material. On the other hand, the stresses well within the plastic zone are governed by the strain-hardening behavior of the more plastically compliant (lower strain-hardening) material. We observe that the extent of the annular zone where the fields are nearly separable (i.e., of the HRR form) is dependent on the remote load combinations and the material combination. When the tractions on the interface are predominantly tensile, there are no indications of crack face contact over any length scale of physical relevance. Instead, the crack tip opens smoothly and crack tip fields as well as the crack opening displacement are scaled by the J-integral. The paper concludes with a discussion on the range of load combinations which could be applied to two fracture test specimen geometries to obtain valid fracture toughness data.

Interaction of Hydrogen Transport and Material Elastoplasticity in Pipeline Steels

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Mohsen Dadfarnia ◽  
Brian P. Somerday ◽  
Petros Sofronis ◽  
Ian M. Robertson ◽  
Douglas Stalheim
Keyword(s):  
Large Scale ◽  
Hydrogen Diffusion ◽  
Crack Tip ◽  
Small Scale ◽  
Material System ◽  
Hydrogen Transport ◽  
Central Production ◽  
Axial Crack ◽  
Scale Yielding ◽  
Hydrogen Accumulation

The technology of large scale hydrogen transmission from central production facilities to refueling stations and stationary power sites is at present undeveloped. Among the problems that confront the implementation of this technology is the deleterious effect of hydrogen on structural material properties, in particular, at gas pressures of the order of 15MPa, which are the suggested magnitudes by economic studies for efficient transport. In order to understand the hydrogen embrittlement conditions of the pipeline materials, we simulate hydrogen diffusion through the surfaces of an axial crack on the internal wall of a vessel coupled with material deformation under plane strain small scale yielding conditions. The calculation of the hydrogen accumulation ahead of the crack tip accounts for stress-driven transient diffusion of hydrogen and trapping at microstructural defects whose density evolves dynamically with deformation. The results are analyzed to correlate for a given material system the time after which hydrogen transport takes place under steady state conditions with the level of load in terms of the applied stress intensity factor at the crack tip and the size of the domain used for the simulation of the diffusion.

Comparison of Strip Yield and Net Section Plasticity Models for a Bar in Bending With a Single Edge Crack

2017 ◽  
Author(s):  
Wolf Reinhardt ◽  
Don Metzger
Keyword(s):  
Edge Crack ◽  
Large Scale ◽  
Stress Singularity ◽  
Crack Tip ◽  
Small Scale ◽  
Single Edge ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tip Plasticity ◽  
Stress And Deformation

The strip yield model is widely used to describe crack tip plasticity in front of a crack. In the strip yield model the stress in the plastic zone is considered as known, and stress and deformation fields can be obtained from elastic solutions using the condition that the crack tip stress singularity vanishes. The strip yield model is generally regarded to be valid to describe small scale plasticity at a crack tip. The present paper examines the behavior of the strip yield model at the transition to large-scale plasticity and its relationship to net section plasticity descriptions. A bar in bending with a single edge crack is used as an illustrative example to derive solutions and compare with one-sided and two-sided plasticity solutions.

Plastic relaxation at a crack tip by asymmetric slip

1988 ◽  
Vol 418 (1854) ◽  
pp. 261-280 ◽  
Keyword(s):  
Slip Band ◽  
Crack Opening ◽  
Crack Tip ◽  
Friction Stress ◽  
Small Scale ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Sharp Crack ◽  
Scale Yielding ◽  
Crack Tip Opening

Relaxation at a sharp crack tip by a single slip band is considered. It is shown that for mixed-mode loading of a plane crack in an isotropic medium there is a unique angle between the slip band and the crack for which the energy release rate (or stress intensity factor) of the crack can be reduced to zero. For such a slip-band calculations are made of the slipband length and the crack-opening displacement as a function of the loading, crack length and friction stress acting on dislocations in the slip band. For small-scale yielding, a simple model is discussed that gives a good approximation to the crack-tip opening displacement and slip-band angle.

Plastic Stress Intensity Factors for Small Scale Yielding in Antiplane Shear by Caustics

1982 ◽  
Vol 49 (4) ◽  
pp. 754-760 ◽  
Author(s):  
P. S. Theocaris ◽  
C. I. Razem
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Antiplane Shear ◽  
Elastic Behavior ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
Plastic Stress

The KIII-stress intensity factor in an edge-cracked plate submitted to antiplane shear may be evaluated by the reflected caustic created around the crack tip, provided that a purely elastic behavior exists at the crack tip [1]. For a work-hardening, elastic-plastic material, when stresses at the vicinity of the crack tip exceed the yield limit of the material, the new shape of caustic differs substantially from the corresponding shape of the elastic solution. In this paper the shape and size of the caustics created at the tip of the crack, when small-scale yielding is established in the vicinity of the crack tip, were studied, based on a closed-form solution introduced by Rice [2]. The plastic stress intensity factor may be evaluated from the dimensions of the plastic caustic. Experimental evidence with cracked plates made of opaque materials, like steel, corroborated the results of the theory.

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.

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