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.

A Dislocation Green’s Function for the Analysis of Multiple Coplanar Cracks or Cracks With Nonuniform Crack Fronts

1990 ◽  
Vol 57 (3) ◽  
pp. 589-595 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Mixed Boundary ◽  
Crack Opening ◽  
Symmetry Plane ◽  
Mode I ◽  
Opening Displacement ◽  
External Crack ◽  
Present Solution ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Coplanar Cracks

This analysis considers the interaction between a penny-shaped crack or a circular external crack and a mode I “opening” point dislocation. The dislocation is taken to lie on the plane of the crack. Symmetry considerations allow the reduction to a mixed boundary value problem for a half space which is solved by well-known methods from potential theory. Closed-form expressions are obtained for the crack opening displacement, stress on the symmetry plane, and the mode I stress intensity factor around the internal or external crack. The use of the present solution for the accurate numerical treatment of cracks with large amplitude variations in the crack front curvature as well as cases of multiple coplanar cracks is outlined.

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.

Determination of cohesive laws in wood bonded joints under mode I loading using the DCB test

Holzforschung ◽  
2013 ◽  
Vol 67 (8) ◽  
pp. 913-922 ◽  
Author(s):  
Filipe G.A. Silva ◽  
Jose Xavier ◽  
Fábio A.M. Pereira ◽  
José J.L. Morais ◽  
Nuno Dourado ◽  
...  
Keyword(s):  
Strain Energy ◽  
Inverse Method ◽  
Strain Energy Release Rate ◽  
Direct Method ◽  
Crack Opening ◽  
Strain Energy Release ◽  
Mode I ◽  
Bonded Joints ◽  
Opening Displacement ◽  
Cohesive Laws

Abstract The cohesive laws (CLs) have been investigated by means of direct and inverse methods concerning wood bonded joints under pure mode I. The experimental results were obtained by tests with double cantilever beam. The direct method is based on the differentiation of the relation between strain energy release rate and crack opening displacement at the crack tip. An equivalent crack method was used to evaluate the strain energy release rate in the course of the test without monitoring the crack length, which is difficult to observe exactly. The crack opening displacement was determined by postprocessing local displacements measured by digital image correlation. The inverse method requires a previous assumption of the CL shape, and as such, a trilinear law with bilinear softening relationship was selected. The cohesive parameters were identified by an optimization procedure involving a developed genetic algorithm. The idea is to minimize an objective function that quantifies the difference between the experimental and the numerical load-displacement curves resulting from the application of a given law. A validation procedure was performed based on a numerical analysis with finite elements. Both methods in focus provided good agreement with the experimental data. It was observed that CLs adopted by the inverse method are consistent with the ones obtained with the direct method.

Crack Opening Area for an Isolated Crack Subjected to a Symmetric Mode I Stress Distribution

2004 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Crack Opening ◽  
Operating Conditions ◽  
Mode I ◽  
Stress Distributions ◽  
Simple Derivation ◽  
Opening Displacement ◽  
System A ◽  
Simplified Procedure ◽  
Leak Before Break

In developing a leak-before-break case for a component in a pressurized system, a key element is an estimation of the size of through-thickness crack that will give a measurable leakage under normal operating conditions, and this requires a knowledge of the crack opening area. In this context, the paper presents a simple derivation of an expression for the crack opening area associated with an isolated crack that is subjected to a general Mode I symmetric tensile stress distribution which could arise from a combination of applied and residual stresses. The paper also presents a simple derivation of an expression for the crack opening displacement at the crack centre which, coupled with the assumption that the crack opening profile conforms to an elliptical shape, has been used as the basis for a simplified procedure for estimating the crack opening area. The resulting expressions are validated by comparing them with known results for specific stress distributions. They are also used to give new results for a cosine stress distribution.

A Two-Parameter Description of the Behaviour of a Process Zone at a Crack Tip: Relation Between the Parameters

2005 ◽  
Author(s):  
E. Smith
Keyword(s):  
Process Zone ◽  
Crack Opening ◽  
Crack Tip ◽  
Relative Displacement ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Power Series Expansions ◽  
Elastic Crack ◽  
Crack Tip Opening ◽  
Crack Faces

The relative displacement of the crack faces and the tensile stress ahead of a Mode I elastic crack tip can be expressed, in the immediate vicinity of the tip, by two-term power series expansions, the two terms being associated with the stress intensity factor KI and a dimensionless parameter g0. These parameters feature prominently in cohesive process zone models of a crack tip with regard to the crack tip opening displacement vT, process zone size s, the crack opening area A and the effective opening area AD of the process zone. This paper shows that KI and g0 depend upon each other via a relation which is dependent upon the geometrical configuration but is independent of the configuration’s loading pattern.

Mode Mixity in the Fracture Toughness Evaluation of Heat-Affected-Zone Material Using SEN(T) Experiment

2021 ◽  
Author(s):  
Sureshkumar Kalyanam ◽  
Yunior Hioe ◽  
Gery Wilkowski
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
Heat Affected Zone ◽  
Crack Opening ◽  
Growth Direction ◽  
Mode I ◽  
Mode Ii ◽  
Mode Mixity ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement

Abstract SEN(T) specimens provide good similitude for surface cracks (SC) in pipes, where a SC structure has lower constraint condition than typically used fracture toughness specimens such as SEN(B) , and C(T). Additionally, the SENT specimen eliminates concern of material anisotropy since the crack growth direction in the SENT is the same as in a surface-cracked pipe. While the existing recommended and industrial practices for SEN(T) have been developed based on assumption of homogenous or mono-material across the crack, their applicability for the evaluation of fracture toughness of heat-affected-zone (HAZ) were evaluated in this investigation. When conducting tests on SEN(T) specimens with prescribed notch/crack in the HAZ, the asymmetric deformation around the crack causes the occurrence of a combination of Mode-I (crack opening) and Mode-II (crack in-plane shearing) behavior. This mode mixity affects the measurement of the crack-tip-opening-displacement (CTOD) and evaluation of elastic-plastic fracture mechanics parameter, J. The CTOD-R curve depicts the change in toughness with crack growth, in a manner similar to the J-R curve methodology. The experimental observations of Mode-I and Mode-II behavior seen in tests of SEN(T) specimens with notch/crack in the HAZ and as the crack propagates through the weld/HAZ thickness were investigated. The issues related to and the changes needed to account for such behavior for the development of recommended practices or standards for SEN(T) testing of weld/HAZ are addressed.

Interaction between a screw dislocation and a bridged crack with surface elasticity

2016 ◽  
Vol 22 (12) ◽  
pp. 2217-2239 ◽  
Author(s):  
Moxuan Yang ◽  
Xu Wang
Keyword(s):  
Screw Dislocation ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Surface Elasticity ◽  
Image Force ◽  
Opening Displacement ◽  
Crack Bridging ◽  
Line Force ◽  
Crack Tips ◽  
Crack Faces

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to a bridging force which is assumed to be proportional to the crack opening displacement, whereas the bridging stiffness is allowed to vary arbitrarily along the crack. By considering a continuous distribution of both screw dislocations and line forces on the crack, the boundary value problem is reduced to two decoupled first-order Cauchy singular integro-differential equations. After the expansion of the unknown line dislocation and line force densities and the known variable bridging stiffness into Chebyshev polynomials, these singular integro-differential equations are solved numerically using the collocation method. Owing to the incorporation of surface elasticity, the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located, whereas in the case when the dislocation is not on the real axis, the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities. The two densities, the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated. We note that crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density. In addition, we demonstrate that both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces. Our results also clearly show that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.

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