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.

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.

scholarly journals Mode II Fracture of an Elastic-Plastic Sandwich Layer

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Emilio Martínez-Pañeda ◽  
I. Iván Cuesta ◽  
Norman A. Fleck
Keyword(s):  
Sandwich Plate ◽  
Numerical Solutions ◽  
Crack Tip ◽  
Mode Ii ◽  
Finite Width ◽  
Yield Model ◽  
Elastic Plastic ◽  
Strip Yield Model ◽  
Finite Crack ◽  
Crack Tip Plasticity

Abstract The shear strength of a pre-cracked sandwich layer is predicted, assuming that the layer is linear elastic or elastic-plastic, with yielding characterized either by the J2 plasticity theory or by a strip-yield model. The substrates are elastic and of dissimilar modulus to that of the layer. Two geometries are analyzed: (i) a semi-infinite crack in a sandwich layer, subjected to a remote mode II K-field and (ii) a center-cracked sandwich plate of finite width under remote shear stress. For the semi-infinite crack, the near-tip stress field is determined as a function of elastic mismatch, and crack tip plasticity is either prevented (the elastic case) or duly accounted for (the elastic-plastic case). Analytical and numerical solutions are then obtained for the center-cracked sandwich plate of the finite width. First, a mode II K-calibration is obtained for a finite crack in the elastic sandwich layer. Second, the analysis is extended to account for crack tip plasticity via a mode II strip-yield model of finite strength and finite toughness. The analytical predictions are verified by finite element simulations, and a failure map is constructed in terms of specimen geometry and crack length.

An Analysis for Crack Instability in Elastically Confined Yielding Regime

1984 ◽  
Vol 106 (4) ◽  
pp. 488-494 ◽  
Author(s):  
A. Zahoor
Keyword(s):  
Control Mode ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Yield Model ◽  
System A ◽  
Strip Yield Model ◽  
Loading System ◽  
Scale Yielding ◽  
Crack Tip Plasticity ◽  
Special Case

An analysis for crack instability is presented which utilizes a J-integral-based tearing modulus approach. In particular, a plane stress center-cracked panel which experiences elastically confined yielding is analyzed for a displacement controlled loading. The analysis assumes a compliant loading system, a special case of which leads to a load control mode of loading. The effects of the crack tip plasticity are taken into account by using the strip-yield model of Dugdale-Barenblatt. A method of predicting the amount of crack growth at the onset of instability is presented. Numerical results suggest that under conditions of small-scale yielding, crack instability can be achieved in materials having very low tearing modulus values.

Strip Yield Analysis for Multiple Cracked Sheet With Riveted Stiffeners

1993 ◽  
Vol 115 (4) ◽  
pp. 398-403 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Plastic Zone ◽  
Stress Singularity ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tips ◽  
Fictitious Crack ◽  
Crack Tip Opening

An elasto-plastic analysis is conducted based upon a strip yield model for analyzing multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown fictitious surface tractions and fastener forces, Fredholm integral equations are formulated from the equilibrium condition along multiple cracks in the sheet. In addition compatibility equations of displacements are formulated among the sheet, fasteners and stiffeners. Based upon no stress singularity at the fictitious crack tips, these equations are iteratively solved as a single system of equations. Then the unknown fictitious surface tractions, fastener forces, and plastic zone sizes ahead of the crack tips are determined. The crack tip opening displacements for a multiple cracked sheet with riveted stiffeners are determined from the derived fictitious surface tractions and plastic zone sizes. Four example calculations and predictions are presented.

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.

Strip-Yield Modeling of Load-Time-Temperature Effects on Crack Growth in Engine Materials

2020 ◽  
Author(s):  
James C. Newman ◽  
Rani Sullivan
Keyword(s):  
Stress Relaxation ◽  
Crack Growth ◽  
Test Data ◽  
Crack Front ◽  
Crack Tip ◽  
Time Dependent ◽  
Yield Model ◽  
Linear Superposition ◽  
Strip Yield Model ◽  
Creep Deformations

Abstract Plastic and creep deformations around a crack front and in the wake of a moving crack under cyclic loading are implemented into the life-prediction code, FASTRAN (a strip-yield model). Creep deformations are modeled by stress relaxation around the crack-tip location, since the crack-front material is under displacement control due to the surrounding elastic material. Sinusoidal and trapezoidal loading are considered. A modified linear superposition model was used to compute the cyclic- and time-dependent damage, which was based on the stress-intensity-factor concept for creep-brittle materials. Application of the modified strip-yield model was made on two sets of test data on Inconel-718 alloy. The environments were laboratory air or helium gas. From the literature, the “environment” had been shown to be a major contributor to damage magnitudes. Thus, the time-dependent crack-growth constants were selected to match the test data. In addition, the effects of a small overload on time-dependent damage, and the effects of stress relaxation and varying temperatures on crack-opening stresses and cyclic crack-tip-opening displacements, were studied.

Strip Yield Analysis on Coalescence of Plastic Zones for Multiple Cracks in a Riveted Stiffened Sheet

1999 ◽  
Vol 121 (3) ◽  
pp. 352-359 ◽  
Author(s):  
Toshihiko Nishimura
Keyword(s):  
Stress Singularity ◽  
Multiple Cracks ◽  
Algebraic Equations ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tips ◽  
Fictitious Crack ◽  
Plastic Zones ◽  
Crack Tip Opening ◽  
Remote Stress

The coalescence conditions of plastic zones are calculated for multiple cracks in a riveted stiffened sheet using a strip yield model. The multiple cracks and their plastic zones are treated as a fictitious crack, and algebraic equations are formulated on compatibility of displacements, no stress singularity at the fictitious crack tips, and zero displacement at the coalesced points of plastic zones. These equations are iteratively solved, and critical values of remote stress, fastener forces, plastic zone sizes, and crack tip opening displacements are calculated. Some numerical results are presented for two cracks in a sheet with and without stiffeners.

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