A Spring Foundation Model for Mode I Failure of Laminated Composites Based on an Energy Criterion

1994 ◽  
Vol 116 (4) ◽  
pp. 512-516 ◽  
Author(s):  
Seung J. Song ◽  
Anthony M. Waas
Keyword(s):  
Laminated Composites ◽  
Current Model ◽  
Crack Opening ◽  
Energy Criterion ◽  
Experimental Results ◽  
Mode I ◽  
Beam Specimen ◽  
Opening Displacement ◽  
Wide Range ◽  
Crack Problems

A mechanical model which can predict mode I delamination failure of laminated composites has been developed. A beam on a nonlinear spring foundation was used to model experimental results obtained from DCB type fracture specimens. The entire thickness of the beam specimen was used as a spring length, and a nonuniform strain distribution throughout the spring length was utilized, based on the 2-D asymptotic solution of the stress field near a crack tip. The failure condition of the spring foundation is based on an energy criterion. Mode I fracture tests were performed to verify the current model using two types of laminated composite DCB specimens. The current model reproduced the experimental results of pulling force versus crack opening displacement curves very closely for a wide range of resin layer thickness of the specimens. The current model has a potential capability of being extended to solve 2-D crack problems, where the evolution of an arbitrary shape of 2-D crack geometry will be predicted as a part of the solution of the current model.

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.

Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

1976 ◽  
Vol 98 (4) ◽  
pp. 289-295 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Stress ◽  
Large Scale ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Strain ◽  
Linear Elastic ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Crack Problems ◽  
Scale Yielding

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

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.

scholarly journals A theory of viscoelastic crack growth-Revisited (Revised)

2021 ◽  
Author(s):  
Richard A Schapery
Keyword(s):  
Crack Growth ◽  
Creep Compliance ◽  
Current Model ◽  
Crack Opening ◽  
Shift Factor ◽  
Analytical Relationship ◽  
Failure Zone ◽  
Opening Displacement ◽  
Linear Elastic Body ◽  
A Minor

Abstract A theory of viscoelastic crack growth developed nearly five decades ago is generalized to allow traction in the so-called failure zone that is a function of the crack opening displacement (COD). In earlier work, except for a minor exception, traction was specified. The current model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship between stress intensity factor and crack speed then follows. Consistent with earlier work, it is defined almost entirely by creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on the crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

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.

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.

Matrix Crack Networks in SiC/SiC Composites: In-Situ Characterisation and Metrics

2021 ◽  
Author(s):  
S. P. Jordan ◽  
S. P. Jeffs ◽  
C. D. Newton ◽  
L. Gale ◽  
P. I. Nicholson ◽  
...  
Keyword(s):  
Crack Opening ◽  
Ceramic Matrix Composites ◽  
Fatigue Loading ◽  
Matrix Crack ◽  
Matrix Cracking ◽  
Damage Development ◽  
Opening Displacement ◽  
Ongoing Research ◽  
Wide Range

Abstract Ceramic matrix composites can offer clear potential for a variety of engineering applications where the temperature capabilities of conventional metals are exceeded. Continued mechanical characterisation is essential to gain an understanding of their associated damage and failure mechanisms across a wide range of representative temperatures. The present paper will report ongoing research to characterize the initiation of matrix cracking at room temperature under tensile stress and subsequent damage development under fatigue loading in a SiCf/SiC composite. Imaging and mechanical property data were obtained via in-situ loading within a scanning electron microscope. The temporal nature of damage development was also recorded through the selective employment of acoustic emission. Metrics to describe the spatial distribution of cracks, crack lengths and crack opening displacement under load will be presented. The inspections also provided detailed evidence of the associated crack closure phenomena. The understanding of matrix crack saturation and matrix/fibre interfacial mechanics will be explored, together with the implications for the use of X-ray tomographic inspection of engineering components during service. The potential for these emergent techniques as a basis for future CMC characterization, via automated image recognition and machine learning, will be highlighted.

Size Dependent Thermo-Piezoelectricity for In-Plane Cracks

2019 ◽  
Vol 827 ◽  
pp. 147-152
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
M. Repka ◽  
Choon Lai Tan
Keyword(s):  
Large Strain ◽  
Crack Opening ◽  
Dielectric Materials ◽  
The Finite Element Method ◽  
Opening Displacement ◽  
Size Dependent ◽  
Symmetric Structure ◽  
Crack Problems ◽  
Conduction Theory ◽  
Fourier Heat Conduction

The finite element method (FEM) is developed to analyse the size effect (flexoeletricity) for 2-D crack problems in thermo-piezoelectricity. Flexoelectricity is observed in micro/nanoelectronic structures, where large strain gradients destroy the symmetric structure of atoms in crystals and thereby causing polarization, even in dielectric materials. In contrast to using classical Fourier heat conduction theory, a finite speed of the thermal wave is considered in the higher order transport equation. The variational principle is applied to derive the FEM equations and C1-continuous elements are employed in the implementation of the FEM. An example is presented to demonstrate the effect of the characteristic time parameter on the crack opening displacement and temperature distribution.

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