Elastic-Plastic Deformation in Surface-Cracked Plates: Experiment and Numerical Analysis

1991 ◽  
Vol 58 (4) ◽  
pp. 895-903 ◽  
Author(s):  
Y.-Y. Wang ◽  
D. M. Parks ◽  
W. R. Lloyd ◽  
W. G. Reuter ◽  
J. Epstein
Keyword(s):  
Crack Front ◽  
Three Dimensional ◽  
Small Strain ◽  
J Integral ◽  
Cracked Plates ◽  
Theory Of Plasticity ◽  
Surface Displacements ◽  
Dominance Study ◽  
Eventual Loss ◽  
Global Deformation

Detailed three-dimensional nonlinear finite element (FE) analyses and experimental moire studies are performed on a plate containing a moderately deep part-through surface crack to establish limits of HRR-dominance. The plate is subjected to predominantly far-field tensile loading. The material under investigation is ASTM A710 steel, which was constitutively modeled by large deformation J2 flow theory of plasticity. The FE mesh was carefully constructed to resolve both crack front fields (such as J-integral and CTOD) and global fields (such as surface displacements, strains). By comparing the J-integral and CTOD results with an earlier HRR-dominance study using (small strain) deformation theory of plasticity, we found little effect of the different formulations on the crack front fields. The global deformation fields from the numerical simulation are in good agreement with our experimental results. The eventual loss of HRR-dominance is intimately related to the interaction of the global plastic flow fields with those of the crack front.

scholarly journals On The Parameters of Geometric Constraints for Cracked Plates under Tension – Three-Dimensional Problems

2017 ◽  
Vol 22 (4) ◽  
pp. 901-919 ◽  
Author(s):  
M. Graba
Keyword(s):  
Fracture Toughness ◽  
Comparative Analysis ◽  
Crack Front ◽  
External Load ◽  
Three Dimensional ◽  
Geometric Constraints ◽  
Numerical Calculations ◽  
Cracked Plates ◽  
The Relationship ◽  
Actual Fracture

Abstract This paper provides a comparative analysis of selected parameters of the geometric constraints for cracked plates subjected to tension. The results of three-dimensional numerical calculations were used to assess the distribution of these parameters around the crack front and their changes along the crack front. The study also involved considering the influence of the external load on the averaged values of the parameters of the geometric constraints as well as the relationship between the material constants and the level of the geometric constraints contributing to the actual fracture toughness for certain geometries.

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.

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

2004 ◽  
Vol 126 (3) ◽  
pp. 293-299 ◽  
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.

On the Path and Area Jx1-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates

2009 ◽  
Vol 417-418 ◽  
pp. 421-424 ◽  
Author(s):  
A. Fernández Canteli ◽  
E. Giner ◽  
D. Fernández Zúñiga ◽  
J. Fernández Sáez
Keyword(s):  
Crack Front ◽  
Three Dimensional ◽  
Young Modulus ◽  
Simple Relation ◽  
Thin Plates ◽  
Elastic Behaviour ◽  
Specimen Thickness ◽  
Plane Stress Condition ◽  
Cracked Plates ◽  
Out Of Plane

In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is shown that the 2D plane stress condition is impossible in the close neighbourhood of a 3D crack front under elastic behaviour so that the consideration of an equivalent Young modulus E', used to find a simple relation between the J(s)-integral and KI for different constraint levels can be misleading.

Formulation of Three-Dimensional J-Integral for Finite Strain Elastic-Plastic Fracture Problems Under Any Load Histories (Monotonic and Cyclic Loads)

2018 ◽  
Author(s):  
Koichiro Arai ◽  
Hiroshi Okada ◽  
Yasunori Yusa
Keyword(s):  
Crack Front ◽  
Integral Domain ◽  
Crack Problem ◽  
Three Dimensional ◽  
Finite Domain ◽  
J Integral ◽  
Proportional Loading ◽  
Numerical Examples ◽  
Elastic Plastic ◽  
Tetrahedral Element

In this paper, a redefined three-dimensional J-integral for the quadratic tetrahedral element along with some numerical examples are presented. It is known that the J-integral represents the energy release rate and can be computed on an arbitrary path or a domain of integration. This feature is called the “path-independent property”. It requires the assumption of proportional loading in the case of elastic-plastic material. Because of this assumption, when the J-integral is applied to a problem under a non-proportional loading condition, the computed J-integral value depends on the integral path or the integral domain. To overcome this problem, the authors have proposed a formula to evaluate the energy dissipation inside a finite domain in the vicinity of the crack front, which is an extension of the conventional three-dimensional J-integral. The energy dissipating into a small but finite domain in the vicinity of crack front includes the energy released due to the opening of new crack faces and the deformation energy in the process zone. The numerical evaluation is carried out by the domain integral. In this formula, it is not necessary to evaluate any non-integrable terms at the crack front. Furthermore, the proposed formula has the feature of integral domain independence for any material models without any assumptions in their deformation histories. Therefore, it is possible to evaluate the J-integral for problems with non-proportional loads by using the proposed method. In this paper, computational method using the quadratic tetrahedral element for the redefined J-integral under non-proportional loading is presented first. Some results of three-dimensional semi-circular surface crack problem are presented as numerical examples.

Fully Plastic Plane Stress Solutions for Biaxially Loaded Center-Cracked Plates

1986 ◽  
Vol 53 (3) ◽  
pp. 555-560 ◽  
Author(s):  
S. Jansson
Keyword(s):  
Fracture Mechanics ◽  
Plane Stress ◽  
Deformation Theory ◽  
Crack Opening ◽  
Small Strain ◽  
Tangential Direction ◽  
Mode I ◽  
J Integral ◽  
Biaxial Testing ◽  
Cracked Plates

Numerical values for the J integral of fracture mechanics, crack opening and load-point displacements are given for stationary cracks in thin quadratic plates where the material is assumed to obey a power-law relation. The plates are loaded biaxially in their own plane under plane stress conditions and the solutions are given under the restriction of small strain and deformation theory. The remote boundaries of the plates are kept straight but free to slide in the tangential direction. This approximates the loading conditions for cruciform specimens with thinner center-sections as used in biaxial testing. It also represents a unit cell in a periodically cracked material. The cracks are loaded in Mode I. The present analysis clarifies the influence of load parallel to the crack and the sensitivity of remote boundary conditions on fracture mechanics parameters.

Elastic-Plastic Constraint Analysis of Semi-Elliptic Surface Cracks in X100 Pipeline Steel

2011 ◽  
Author(s):  
Z. X. Wang ◽  
R. F. Zhang ◽  
Y. J. Chao ◽  
P. S. Lam
Keyword(s):  
Free Surface ◽  
Crack Front ◽  
Driving Force ◽  
Pipeline Steel ◽  
Three Dimensional ◽  
Elliptic Crack ◽  
J Integral ◽  
Surface Cracks ◽  
Crack Driving Force ◽  
X100 Pipeline Steel

In the framework of the J-A2 fracture theory, the crack driving force J and the crack tip constraint parameter A2 are used to describe the near crack tip stress and deformation fields. These two parameters, J and A2, were calculated from three-dimensional finite element results for semi-elliptic surface cracks with various lengths and depths in X100 pipeline steel. It was found that, under a uniform far field tensile loading, A2 increases rapidly to a nearly constant value along the crack front from the free surface to the deepest part of the crack. A similar trend was found for the J-integral distribution except in the case of a semi-circular crack. In addition, for a given elliptic crack configuration, A2 showed significant J-integral dependence when the crack front approached the free surface, where a strong three-dimensional effect is apparent. On the other hand, at the deepest part of the crack, A2 converged to a constant value. Two-dimensional plane strain calculations were also performed for single edge-notched tension specimens (SENT), where the crack length corresponds to the depth of the surface crack. The constraint of these two configurations (semi-elliptic crack and SENT) were compared under the same crack driving force (J-integral). In general, the constraint at the deepest crack front of an elliptic crack is higher than that of the corresponding SENT, especially in mid- to large scale yielding condition where J-integral is relatively large. It can be concluded that using fracture toughness determined from SENT specimens to predict surface flaw stability may lead to non-conservative result.

scholarly journals Visualization of the Strain-Rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

2019 ◽  
Vol 9 (14) ◽  
pp. 2920
Author(s):  
Lorena Salazar-Llano ◽  
Camilo Bayona-Roa
Keyword(s):  
Strain Rate ◽  
Temporal Change ◽  
Three Dimensional ◽  
Urban System ◽  
Deformation Pattern ◽  
Analysis Methodology ◽  
Global Deformation ◽  
Temporal Rate ◽  
Cloud Of Points ◽  
Entire Dataset

One challenging problem is the representation of three-dimensional datasets that vary with time. These datasets can be thought of as a cloud of points that gradually deforms. However, point-wise variations lack information about the overall deformation pattern, and, more importantly, about the extreme deformation locations inside the cloud. This present article applies a technique in computational mechanics to derive the strain-rate state of a time-dependent and three-dimensional data distribution, by which one can characterize its main trends of shift. Indeed, the tensorial analysis methodology is able to determine the global deformation rates in the entire dataset. With the use of this technique, one can characterize the significant fluctuations in a reduced multivariate description of an urban system and identify the possible causes of those changes: calculating the strain-rate state of a PCA-based multivariate description of an urban system, we are able to describe the clustering and divergence patterns between the districts of a city and to characterize the temporal rate in which those variations happen.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

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