Three-Dimensional Effects Near a Crack Tip in a Ductile Three-Point Bend Specimen: Part I—A Numerical Investigation

1990 ◽  
Vol 57 (3) ◽  
pp. 607-617 ◽  
Author(s):  
R. Narasimhan ◽  
A. J. Rosakis
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Crack Front ◽  
Three Dimensional ◽  
Crack Tip ◽  
Upper And Lower Bounds ◽  
Thickness Variation ◽  
Bend Specimen ◽  
Dimensional Effects ◽  
Point Bend

A simultaneous numerical and experimental investigation is undertaken to assess three-dimensional effects and HRR dominance near a crack front in a ductile 3-point bend specimen. In parallel to the three-dimensional calculations, a plane-strain and a plane-stress analysis of the same in-plane specimen geometry is performed to obtain upper and lower bounds for the three-dimensional calculation. The radial, angular, and thickness variation of the stresses and displacements are studied in great detail from contained yielding to fully plastic conditions. The results indicate that the plane-strain HRR field prevails in the interior of the specimen very near the crack front even for moderate extents of yielding. On the other hand, for distances from the crack tip exceeding about half a specimen thickness, plane-stress conditions are approached. The calculations presented here model a series of laboratory experiments involving three independent experimental techniques. Details regarding the experiments and comparisons of the experimental measurements with numerical calculations and theory are emphasized in Part II of this work.

Three-Dimensional Effects Near a Crack Tip in a Ductile Three-Point Bend Specimen: Part II—An Experimental Investigation Using Interferometry and Caustics

1990 ◽  
Vol 57 (3) ◽  
pp. 618-626 ◽  
Author(s):  
Alan T. Zehnder ◽  
Ares J. Rosakis
Keyword(s):  
Experimental Investigation ◽  
Large Scale ◽  
Three Dimensional ◽  
Time History ◽  
Fracture Initiation ◽  
Optical Methods ◽  
J Integral ◽  
Bend Specimen ◽  
Dimensional Effects ◽  
Point Bend

An experimental investigation is undertaken to assess three-dimensional effects near a crack front in a ductile three-point bend specimen. The possibility of using the optical method of caustics for the measurement of the J-integral in the presence of large-scale yielding and three-dimensional fields is also investigated. Experiments using the optical methods of caustics by reflection and Twyman-Green interferometry are performed simultaneously on either side of the test specimen. The load and load-point displacement are also measured. The experimental results are compared with very good agreement to the results of a finite element simulation of the experiment. The caustics experiments are used to obtain a calibration relation between the value of the J-integral and the caustic diameter for load levels up to fracture initiation. It is proposed that such a calibration be used in dynamic fracture initiation experiments for the measurement of the time history of the dynamic J-integral.

Analysis of the Three-Dimensional Zone around the Interfacial Crack Tip: The K-Influence Domain Range in the Plane Stress State

2017 ◽  
Vol 754 ◽  
pp. 119-122
Author(s):  
Jelena M. Djoković ◽  
Snežana D. Vulović ◽  
Ružica R. Nikolić ◽  
Miroslav M. Živković ◽  
Branislav Hadzima
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress State ◽  
Intensity Factor ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Crack Tip ◽  
Plane Stress State ◽  
Relevant Parameter

The bimaterial sample was analyzed to determine the three-dimensional zone at the interface crack tip and the field in the plane stress state. The solutions for the complete 3D field in different zones around the crack tip were approximated by the plane stress and plane strain states' asymptotic solutions. The difference between the solutions for the plane stress and plane strain states is defined by the three variables. The established relationship between the far field and the field around the crack tip in the plane strain conditions, enables relating the measured experimental results of the stress intensity factor to results for the stress intensity factor for the field around the crack tip, which represent the more relevant parameter for formulating the fracture criterion.

Influence of Porosity on Plane Strain Tensile Crack-Tip Stress Fields in Elastic-Plastic Materials: Part I

1992 ◽  
Vol 59 (3) ◽  
pp. 559-567 ◽  
Author(s):  
W. J. Drugan ◽  
Y. Miao
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Normal Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Entire Range ◽  
Crack Tip ◽  
Constant Stress ◽  
Tensile Crack ◽  
Stress Discontinuity

We perform an analytical first study of the influence of a uniform porosity distribution, for the entire range of porosity level, on the stress field near a plane strain tensile crack tip in ductile material. Such uniform porosity distributions (approximately) arise in incompletely sintered or previously deformed (e.g., during processing) ductile metals and alloys. The elastic-plastic Gurson-Tvergaard constitutive formulation is employed. This model has a sound micromechanical basis, and has been shown to agree well with detailed numerical finite element solutions of, and with experiments on, voided materials. To facilitate closed-form analytical results to the extent possible, we treat nonhardening material with constant, uniform porosity. We show that the assumption of singular plastic strain in the limit as the crack tip is approached renders the governing equations statically determinate with two permissible types of near-tip angular sector: one with constant Cartesian components of stress (“constant stress”); and one with radial stress characteristics (“generalized centered fan”). The former admits an exact asymptotic closed-form stress field representation, and although we prove the latter does not, we derive a highly accurate closed-form approximate representation. We show that complete near-tip solutions can be constructed from these two sector types for the entire range of porosity. These solutions are comprised of three asymptotic sector configurations: (i) “generalized Prandtlfield”for low porosities (0 ≤ f ≤ .02979), similar to the plane strain Prandtl field of fully dense materials, with a fully continuous stress field but sector extents that vary with porosity; (ii) “plane-stress-like field” for intermediate porosities (.02979 < f < .12029), resembling the plane stress solution for fully dense materials, with a ray of radial normal stress discontinuity but sector extents that vary with porosity; (iii) two constant stress sectors for the remaining high porosity range, with a ray of radial normal stress discontinuity and fixed sector extents. Among several interesting features, the solutions show that increasing porosity causes significant modification of the angular variation of stress components, particularly for a range of angles ahead of the crack tip, while also causing a drastic reduction in maximum hydrostatic stress level.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

2003 ◽  
Author(s):  
Y. Kim ◽  
Y. J. Chao ◽  
M. J. Pechersky ◽  
M. J. Morgan
Keyword(s):  
Fracture Toughness ◽  
Plane Strain ◽  
Crack Front ◽  
Testing Effect ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
J Integral ◽  
Η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Computational Modelling of High Temperature Steady State Crack Growth Using a Damage-Based Approach

2003 ◽  
Author(s):  
Masataka Yatomi ◽  
Noel P. O’Dowd ◽  
Kamran M. Nikbin
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Computational Study ◽  
Creep Crack Growth ◽  
Computational Modelling ◽  
Crack Tip ◽  
Creep Damage ◽  
Creep Model ◽  
Manganese Steel

In this work a computational study of creep crack growth in a carbon manganese steel is presented. The constitutive behaviour of the steel is described by a power law creep model and the accumulation of creep damage is accounted for through the use of a well-established model for void growth in creeping materials. Two dimensional finite element analyses have been performed for a compact tension specimen and it has been found that the predicted crack growth rate under plane strain conditions approaches that under plane stress conditions at high C* levels. Furthermore it has been shown, both experimentally and numerically, that an increase in test temperature causes the convergence of the cracking rate to occur at higher values of C*. This trend may be explained by the influence of crack-tip plasticity, which reduces the relative difference in constraint between plane stress and plane strain conditions. The constraint effect has been quantified through the use of a two-parameter characterisation of the crack tip fields under creep conditions.

Three-Dimensional Elastic Stress Fields of Finite Thickness Plates with Elliptical Hole

2007 ◽  
Vol 353-358 ◽  
pp. 74-77
Author(s):  
Zheng Yang ◽  
Chong Du Cho ◽  
Ting Ya Su ◽  
Chang Boo Kim ◽  
Hyeon Gyu Beom
Keyword(s):  
Stress Concentration ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Three Dimensional

Based on detailed three-dimensional finite element analyses, elastic stress and strain field of ellipse major axis end in plates with different thickness and ellipse configurations subjected to uniaxial tension have been investigated. The plate thickness and ellipse configuration have obvious effects on the stress concentration factor, which is higher in finite thickness plates than in plane stress and plane strain cases. The out-of-plane stress constraint factor tends the maximum on the mid-plane and approaches to zero on the free plane. Stress concentration factors distribute ununiformly through the plate thickness, the value and location of maximum stress concentration factor depend on the plate thickness and the ellipse configurations. Both stress concentration factor in the middle plane and the maximum stress concentration factor are greater than that under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one undergone plane stress or plane strain. For the sharper notch, the influence of three-dimensional stress state on the SCF must be considered.

Elastic-plastic J-Tz dominance in bending and tension loadings

2019 ◽  
Vol 10 (5) ◽  
pp. 644-659
Author(s):  
Feizal Yusof ◽  
Karh Heng Leong
Keyword(s):  
Crack Length ◽  
Power Law ◽  
Crack Front ◽  
Three Dimensional ◽  
Crack Tip ◽  
Content Type ◽  
Elastic Plastic ◽  
Crack Tip Fields ◽  
Out Of Plane ◽  
Crack Tip Stress

Purpose Crack tip stresses are used to relate the ability of structures to perform under the influence of cracks and defects. One of the methods to determine three-dimensional crack tip stresses is through the J-Tz method. The J-Tz method has been used extensively to characterize the stresses of cracked geometries that demonstrate positive T-stress but limited in characterizing negative T-stresses. The purpose of this paper is to apply the J-Tz method to characterize a three-dimensional crack tip stress field in a changing crack length from positive to negative T-stress geometries. Design/methodology/approach Elastic-plastic crack border fields of deep and shallow cracks in tension and bending loads were investigated through a series of three-dimensional finite element (FE) and analytical J-Tz solutions for a range of crack lengths ranging from 0.1⩽a/W⩽0.5 for two thickness extremes of B/(W − a)=1 and 0.05. Findings Both the FE and the J-Tz approaches showed that the combined in-plane and the out-of-plane constraint loss were differently affected by the T-stress and the out-of-plane size effects when the crack length changed from deep to shallow cracks. The conditions of the J-Tz dominance on the three-dimensional crack front tip were shown to be limited to positive T-stress geometries, and the J-Tz-Q2D approach can extend the crack border dominance of the three-dimensional deep and shallow bend models along the crack front tip until perturbed by an elastic-plastic corner field. Practical implications The paper reports the limitation of the J-Tz approach, which is used to calculate the state of three-dimensional crack tip stresses in power law hardening materials. The results from this paper suggest that the characterization of the three-dimensional crack tip stress in power law hardening materials is still an open issue and requires other suitable solutions to solve the problem. Originality/value This paper demonstrates a thorough analysis of a three-dimensional elastic-plastic crack tip fields for geometries that are initially either fully constrained (positive T-stress) or unconstrained (negative T-stress) crack tip fields but, subsequently, the T-stress sign changes due to crack length reduction and specimen thickness increase. The J-Tz stress-based method has been tested and its dominance over the crack tip field is shown to be affected by the combined in-plane and the out-of-plane constraints and the corner field effects.

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