A three-parameter method for determining stress intensity factors from isochromatic fringe loops

1978 ◽  
Vol 13 (2) ◽  
pp. 91-94 ◽  
Author(s):  
J M Etheridge ◽  
J W Dally
Keyword(s):  
Stress Intensity ◽  
Maximum Shear Stress ◽  
Crack Problem ◽  
Crack Tip ◽  
Parameter Method ◽  
Intensity Factors ◽  
Isochromatic Fringe ◽  
Method Of Solution ◽  
Parameter Approach ◽  
Two Parameter

Methods for determining the stress intensity factor, K, from isochromatic fringe loops obtained from photoelastic models with sharp cracks are briefly reviewed. A new three-parameter method is introduced which follows the two-parameter approach developed previously by Irwin. In the three-parameter method, three different terms in an analytical solution are adjusted to obtain a suitable match between the theoretical and experimental isochromatic loops. The three parameters are: K/√2πz, which describes the crack-tip singularity, ( b) β K/√z, to account for variations in the stress field removed from the crack tip and ( c) σoa = α1 K/√2πa, which is added to the σ x component of the stres field to account for the biaxiality of the far-field stresses. A relationship is derived for the maximum shear stress, τm, in terms of the three fitting parameters ( K, α, and β) and the two geometric parameters ( rm and θm) associated with the isochromatic fringe loops. A method of solution based on measurements of rm and θm from any two independent fringe loops is given. The accuracy of the three-parameter method was determined by using exact results from the central crack problem for a standard. It was found that the error was within ± 1 per cent for 69° < θm < 145°. Comparison with the two-parameter method shows that the three-parameter method is more accurate and is applicable over a wider range of θm.

The Dynamic Three-Parameter Method for Determination of Stress-Intensity Factors From Dynamic Isochromatic Crack-Tip Stress Patterns

1980 ◽  
Vol 47 (4) ◽  
pp. 795-800 ◽  
Author(s):  
H. P. Rossmanith
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Correction Term ◽  
Crack Tip ◽  
Higher Order ◽  
Parameter Method ◽  
Intensity Factors ◽  
Higher Order Terms ◽  
Stress Patterns

Correction methods for the determination of dynamic stress-intensity factors from isochromatic crack-tip stress patterns are developed within the framework of a Westergaard-type stress-function analysis where higher-order terms of the series expansions of the stress functions are retained. The addition σox to the extensional stress σx, is regarded as a first correction term, and the far-field correction term which is proportional to r1/2 is referred to as the β-correction. The β-term represents effects that are due to particular loading systems and situations including finite specimen boundaries. The associated method to determine K can be termed a three-parameter method since it contains K, α, and β as parameters. The correction methods, i.e., velocity correction and higher-order term corrections, permit modification of the “static” crack velocity versus stress-intensity factor (c-K) relationship by correcting the static K for the influence of crack speed and higher-order terms. The results show that both corrections assist the interpretation of current photoelastic c-K-data even though the crack speeds do not exceed one third of the shear wave speed.

scholarly journals The Crack Problem in Bonded Nonhomogeneous Materials

1991 ◽  
Vol 58 (2) ◽  
pp. 410-418 ◽  
Author(s):  
F. Erdogan ◽  
A. C. Kaya ◽  
P. F. Joseph
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Plane Elasticity ◽  
Primary Objective ◽  
Intensity Factors ◽  
Shear Moduli ◽  
Square Root Singularity

In this paper the plane elasticity problem for two bonded half-planes containing a crack perpendicular to the interface is considered. The primary objective of the paper is to study the effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors. The two materials are, thus, assumed to have the shear moduli μ0 and μ0exp(βx), x = 0 being the diffusion plane. Of particular interest is the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r−α, 0<α<1, in this problem the stresses have a standard square root singularity regardless of the location of the crack tip. The nonhomogeneity constant β has, however, considerable influence on the stress intensity factors.

Experimental Determination Technique of Stress Intensity Factor and Its Application

1989 ◽  
Vol 111 (1) ◽  
pp. 81-86 ◽  
Author(s):  
Y. Z. Itoh ◽  
T. Murakami ◽  
H. Kashiwaya
Keyword(s):  
Stress Intensity ◽  
Strain Gage ◽  
Stress Intensity Factors ◽  
Fracture Behavior ◽  
Crack Problem ◽  
Crack Tip ◽  
Intensity Factors ◽  
Extrapolation Technique ◽  
Polymer Sheets ◽  
Special Strain

The proportional extrapolation technique is proposed for determining experimentally and accurately stress intensity factors, using the crack tip stresses measured by strain gage. The technique is based on the assumption that the effects of gage length and width on the measurement of the crack tip stresses are corrected by comparing with standard problems, and the corrected results are only accurate in the limit as r→0 (r; distance from crack tip). A special strain gage pattern was developed for applying the proportional extrapolation technique. The stress intensity factors of a two-dimensional crack problem were analyzed using this strain gage, and as an application example, the fracture behavior under mixed mode loading was investigated on notched polymer sheets.

scholarly journals Dynamic Mixed Mode I-II Crack Kinking Under Oblique Stress Wave Loading in Brittle Solids

1990 ◽  
Vol 57 (1) ◽  
pp. 117-127 ◽  
Author(s):  
Chien-Ching Ma
Keyword(s):  
Stress Intensity ◽  
Stress Wave ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Elastic Solid ◽  
Perturbation Parameter ◽  
Intensity Factors ◽  
Linear Superposition ◽  
Dynamic Stress Intensity Factors ◽  
Brittle Solids

The dynamic stress intensity factors of an initially stationary semi-infinite crack in an unbounded linear elastic solid which kinks at some time tf after the arrival of a stress wave is obtained as a function of kinking crack tip velocity v, kinking angle δ, incident stress wave angle α, time t, and the delay time tf. A perturbation method, using the kinking angle δ as the perturbation parameter, is used. The method relies on solving simple problems which can be used with linear superposition to solve the problem of a kinked crack. The solutions can be compared with numerical results and other approximate results for the case of tf = 0 and give excellent agreement for a large range of kinking angles. The elastodynamic stress intensity factors of the kinking crack tip are used to compute the corresponding fluxes of energy into the propagating crack-tip, and these results are discussed in terms of an assumed fracture criterion.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

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