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.

Bending Modified J-Q Theory and Its Application to Fracture Constraint Analysis

2007 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Brian N. Leis
Keyword(s):  
Pipeline Steel ◽  
Crack Tip ◽  
Bending Stress ◽  
Single Edge ◽  
X80 Pipeline Steel ◽  
Q Theory ◽  
Constraint Analysis ◽  
Scale Yielding ◽  
Crack Tip Constraint ◽  
Fracture Constraint

The J-Q theory [1,2] can characterize the crack-tip fields and quantify fracture constraints for various geometric and loading configurations in elastic-plastic materials, but it fails to do so for bending-dominant geometries at large-scale yielding (LSY). This issue significantly restricts its applications to fracture constraint analysis. A modification of the J-Q theory is thus proposed in this paper as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear global bending stress is linearly approximated in the region of interest at LSY. To verify the bending-modified J-Q solution, detailed elastic-plastic finite element analysis (FEA) is carried out under plane strain conditions for three conventional bending specimens, i.e., single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens for X80 pipeline steel. Deformation considered varies from small-scale yielding (SSY) to LSY. The results show that the bending modified J-Q solution can well match FEA results of crack-tip stress fields for the bending specimens at all deformation levels from SSY to LSY, and the modified parameter Q is a load- and distance-independent constraint parameter at LSY. Thus, the modified parameter Q can be effectively used to quantify the crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by ranking crack-tip constraint levels for fracture specimens and by determining constraint corrected J-R curves for the X80 pipeline steel.

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.

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.

JEDI: A Code for the Calculation of J for Cracks Inserted in Initial Strain Fields and the Role of J and Q in the Prediction of Crack Extension and Fracture

2008 ◽  
Author(s):  
David W. Beardsmore
Keyword(s):  
Fracture Toughness ◽  
Strain Field ◽  
Crack Extension ◽  
Crack Tip ◽  
Initial Strain ◽  
Small Scale ◽  
Assessment Procedure ◽  
Crack Tip Fields ◽  
Crack Tip Constraint ◽  
Inelastic Strains

When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.

Numerical Analyses of Ductile Fracture Behavior in 2D Plane Strain and Axisymmetric Models Using the Complete Gurson Model

2009 ◽  
Author(s):  
Jie Xu ◽  
Zhiliang Zhang ◽  
Erling O̸stby ◽  
Ba˚rd Nyhus ◽  
Dongbai Sun
Keyword(s):  
Crack Growth ◽  
Fracture Behavior ◽  
Large Scale ◽  
Crack Tip ◽  
Ductile Crack ◽  
Geometry Dependence ◽  
Ductile Crack Growth ◽  
Scale Yielding ◽  
Resistance Curves ◽  
Crack Tip Constraint

Ductile crack growth plays an important role in the analyses of fracture behavior of structures. A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding conditions. This geometry dependence is associated with different levels of crack tip constraint. However, an independent relationship between the fracture resistance and crack tip constraint has also been observed in experimental studies for selected specimen geometries. To verify these results, crack growth resistance curves for plane strain, mode I crack growth under large scale yielding have been computed using the complete Gurson model. Single edge notched bending (SENB) and tension (SENT) specimens with three different crack geometries have been selected for the numerical analyses. Specimen size effect on ductile crack growth behavior has also been studied. In addition, the SENT specimen appears as an alternative to conventional fracture specimens to characterize fracture toughness of circumferentially cracked pipes due to its similar geometry constraint ahead of the crack tip with that of cracks in pipes. 2D axisymmetric models have been carried out to investigate the effect of biaxial loading (axial tension combined with internal pressure) on the resistance curves for pipes with long internal circumferential cracks under large scale yielding conditions.

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.

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.

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