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.

Fracture Mechanics of Periodic Multilayers With Different Microstructural Scales and Moduli Contrast

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Linfeng Chen ◽  
Marek-Jerzy Pindera
Keyword(s):  
Fracture Mechanics ◽  
Crack Opening ◽  
Strain Energy Release ◽  
Computational Effort ◽  
Mode I ◽  
Preliminary Calculation ◽  
Opening Displacement ◽  
Microstructural Refinement ◽  
Loading Mode ◽  
Microstructural Effects

In a recent investigation of microstructural effects in finite periodic multilayers, we have shown that under Mode I loading, the crack-opening displacement approaches that of the same crack in an equivalent homogenized material as the microstructure comprised of alternating stiff and soft layers becomes increasingly finer. In contrast, Mode I stress intensity factor asymptotically converges to values that depend on the stiffness of the cracked layer. Preliminary calculation of Mode I strain energy release rate as a function of the microstructural refinement suggested that this may be a better fracture mechanics parameter for assessing fracture toughness of periodic layered media. Herein, we extend the above investigation by considering both Mode I and II loading to study the effect of layer modulus ratio on fracture mechanics parameters as a function of microstructural refinement. The previously introduced concept of partial homogenization of the microstructure sufficiently far from the crack is also pursued in order to gauge its efficiency in correctly capturing fracture mechanics parameters with a minimum of computational effort. The fracture mechanics parameters are shown to be influenced by the local microstructure to an extent that depends on the layer modulus mismatch. An accurate calculation of these parameters requires the retention of several layers adjacent to the affected cracked layer whose number depends on the modulus mismatch and loading mode.

Fracture Mechanics

1983 ◽  
pp. 269-293
Author(s):  
R. L. Tobler ◽  
H. I. McHenry
Keyword(s):  
Fracture Mechanics ◽  
Crack Opening Displacement ◽  
Low Temperatures ◽  
Fracture Behavior ◽  
Crack Opening ◽  
J Integral ◽  
Cryogenic Temperatures ◽  
Testing Methods ◽  
Opening Displacement ◽  
The Many

Abstract This chapter reviews the concepts of fracture mechanics and their application to materials evaluation and the design of cryogenic structures. Emphasis is placed on an explanation of technology, a review of fracture mechanics testing methods, and a discussion on the many factors contributing to the fracture behavior of materials at cryogenic temperatures. Three approaches of elastic-plastic fracture mechanics are covered, namely the crack opening displacement, the J-integral, and the R-curve methods. The chapter also discusses the influence of thermal and metallurgical effects on toughness at low temperatures.

Towards a Process for the Assessment of Mixed Mode I+II Fracture Toughness

2018 ◽  
Author(s):  
Afaf Bouydo ◽  
Valéry Lacroix ◽  
Rachid Chaouadi ◽  
Vratislav Mares
Keyword(s):  
Fracture Toughness ◽  
Mixed Mode ◽  
Ferritic Steel ◽  
Crack Opening ◽  
Pressure Vessels ◽  
Mode I ◽  
J Integral ◽  
Mode I Crack ◽  
Standard Mode ◽  
Material Fracture

In fracture mechanics, a flaw behavior in pressure vessels is assessed with respect to the material fracture toughness. Fracture toughness which most Fitness-for-Service (FFS) codes relies on, only considers mode-I crack opening. However, in presence of tilted flaws, like quasi-laminar hydrogen flakes, this mode-I toughness may be too severe, and a mixed mode I+II fracture toughness seems to be more appropriate. In order to address the assessment of the fracture toughness curve, mixed mode I+II tests were performed by the authors on ferritic steel samples by adjusting the standard mode I CT specimen geometry to a geometry subjected to mixed mode I+II. Then, XFEM simulations of the mixed mode tests were performed in order to calculate the J-integral along the crack front. Based on tests and calculations results, the paper explains how the authors work towards proposing a method to measure the material fracture toughness in case of flaws subjected to mixed mode (I+II) loading.

Universal J-Integral to Assess Multiaxial Low Cycle Fatigue

2006 ◽  
Author(s):  
Takamoto Itoh ◽  
Masao Sakane ◽  
Dimitar Tchankov ◽  
Naomi Hamada
Keyword(s):  
Crack Opening Displacement ◽  
Low Cycle Fatigue ◽  
Crack Opening ◽  
304 Stainless Steel ◽  
Nickel Base Superalloy ◽  
Mode I ◽  
J Integral ◽  
Mode I Crack ◽  
Cycle Fatigue ◽  
Opening Displacement

This paper proposes the universal J-integral for correlating multiaxial low cycle fatigue lives, utilizing the crack opening displacement approach. The universal J-integral is a function of Young’s modulus, yield stress, strain biaxiality and specimen geometry, so that it is not necessary to conduct multiaxial low cycle fatigue tests to determine the universal J-integral. To derive the universal J-integral, J-integral for a biaxially loaded Mode I crack was equated with the equivalent strain based on crack opening displacement (COD strain). The COD strain is a parameter to express the strain intensity ahead of a Mode I crack subjected to biaxial strains, normal and parallel to the crack. The J-integral was shown to be a suitable parameter for correlating crack propagation rates in the biaxial straining conditions. The J-integral was extended to a parameter, named the universal J-integral, to correlate multiaxial low cycle fatigue lives, taking account of the material dependency. The universal J-integral successfully correlated the multiaxial low cycle fatigue lives of type 304 stainless steel, Cr-Mo-V steel, Inconel 738 LC nickel base superalloy and Sn-37Pb eutectic solder universally within a factor of three scatter band independent on the material.

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.

A Study on Governing Parameters to Improve the Results of Caustic Applied to Mode-I Fracture Mechanics Problems

1994 ◽  
Vol 23 (1) ◽  
pp. 1-11 ◽  
Author(s):  
P. Rathinam ◽  
R. Narayanan ◽  
G. Jayarama Rao
Keyword(s):  
Fracture Mechanics ◽  
Mode I ◽  
Mode I Fracture

A mode I crack with multiple islands of ideal contact between the crack faces: An asymptotic model

2021 ◽  
pp. 108128652110214
Author(s):  
Ivan Argatov
Keyword(s):  
Crack Opening ◽  
Reduction Factor ◽  
Mode I ◽  
Asymptotic Model ◽  
Mode I Crack ◽  
Opening Displacement ◽  
Multiple Contacts ◽  
Scaling Hypothesis ◽  
Penny Shaped Crack ◽  
Crack Faces

The problem of a mode I crack having multiple contacts between the crack faces is considered. In the case of small contact islands of arbitrary shapes, which are arbitrarily located inside the crack, the first-order asymptotic model for the crack opening displacement is constructed using the method of matched asymptotic expansions. The case of a penny-shaped crack has been studied in detail. A scaling hypothesis for the compliance reduction factor is formulated.

scholarly journals Fracture Mechanical Analysis of Thin-Walled Cylindrical Shells with Cracks

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 592
Author(s):  
Feng Yue ◽  
Ziyan Wu
Keyword(s):  
Fracture Mechanics ◽  
Tensile Stress ◽  
Failure Modes ◽  
Cylindrical Shells ◽  
Crack Tip ◽  
Mechanical Analysis ◽  
J Integral ◽  
Thin Walled Structures ◽  
Circumferential Tensile Stress ◽  
Thin Walled

The fracture mechanical behaviour of thin-walled structures with cracks is highly significant for structural strength design, safety and reliability analysis, and defect evaluation. In this study, the effects of various factors on the fracture parameters, crack initiation angles and plastic zones of thin-walled cylindrical shells with cracks are investigated. First, based on the J-integral and displacement extrapolation methods, the stress intensity factors of thin-walled cylindrical shells with circumferential cracks and compound cracks are studied using linear elastic fracture mechanics, respectively. Second, based on the theory of maximum circumferential tensile stress of compound cracks, the number of singular elements at a crack tip is varied to determine the node of the element corresponding to the maximum circumferential tensile stress, and the initiation angle for a compound crack is predicted. Third, based on the J-integral theory, the size of the plastic zone and J-integral of a thin-walled cylindrical shell with a circumferential crack are analysed, using elastic-plastic fracture mechanics. The results show that the stress in front of a crack tip does not increase after reaching the yield strength and enters the stage of plastic development, and the predicted initiation angle of an oblique crack mainly depends on its original inclination angle. The conclusions have theoretical and engineering significance for the selection of the fracture criteria and determination of the failure modes of thin-walled structures with cracks.

Fracture Mechanics Method for Mode-I Interface Evaluation of FRP Bonded to Concrete Substrates

2006 ◽  
Vol 18 (5) ◽  
pp. 732-742 ◽  
Author(s):  
Julio F. Davalos ◽  
Shilpa S. Kodkani ◽  
Indrajit Ray
Keyword(s):  
Fracture Mechanics ◽  
Mode I
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