by Tsukrov, Igor; Kachanov, Mark

Effective moduli of a 2-D anisotropic solid with elliptical holes of an arbitrary (non-random) orientational distribution are given in closed form. The results are derived in the non-interacting approximation – the basic building block for various approximate schemes. Proper tensorial parameters of defect density are identified.

DOI: 10.1023/A:1007598017845
Print publication date: 7/1/1998
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by Sevostianov, Igor; Kachanov, Mark

The relationship between microstructure of the cortical bone and its effective elastic properties is discussed. We utilize results of Kachanov et al (1994) on materials with cracks/pores of diverse shapes. Bone’s microstructure is modeled using available micrographs. The calculated anisotropic elastic constants for porous cortical bone are compared with available experimental data. For Young’s moduli and shear moduli the agreement is good, whereas Poisson’s ratios differ significantly. Possible reasons for this difference are discussed.

DOI: 10.1023/A:1007593916936
Print publication date: 7/1/1998
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by Massabò, Roberta; Mumm, Daniel R.; Cox, Briann

This paper deals with characterizing the bridging mechanisms developed across delamination cracks by through-thickness reinforcement, using stitched carbon/epoxy laminates under mode II loading as a prime example. End Notched Flexure (ENF) tests are performed which show that stitching can provide stable crack growth. The bridging law, which characterizes the bridging action of the stitches, is deduced from both crack profile measurements and load vs. deflection curves. Consistent results are obtained from the two methods. The inferred laws imply that delamination cracks will commonly grow in conditions that are neither accurately nor properly described by linear elastic fracture mechanics. Large scale bridging calculations are required, in which the essential material property is the bridging traction law. The level of detail in which the law must be determined can be inferred from the sensitivity of predicted crack growth to variations in the law. It is recommended that the required parametric traction law be deduced in engineering practice from load vs. deflection data from the standard ENF (or similar) test, with due regard to selecting the notch size and other specimen dimensions to ensure that crack growth is stable in the test.

DOI: 10.1023/A:1007520324207
Print publication date: 7/1/1998
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by Xu, Shilang; Reinhardt, Hans W.

The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss–Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (K_R-curves) were determined by combining the crack initiation toughness
$$K_{ Ic}^{ini} $$
that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing K_R-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve(K_R-curve) is lower than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers.

DOI: 10.1023/A:1007553012684
Print publication date: 7/1/1998
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by Meng, Lu; Lee, S.B.

The objective of this paper is to study the eigenspectrum of a creeping body with a static mode I crack. The coordinate perturbation technique is employed to pose the required asymptotic equations. To attain eigensolutions a numerical scheme is worked out and the results obtained provide the information including the number of singularities, and their orders, as well as the angular distributions of stresses. In particular, additional eigenvalues of the HRR/RR problem that have not been reported previously are presented in the context, indicating the fact that other singular fields may exist for the problem. The discussion is also performed to the higher order asymptotic solutions that differ from those resulting from the eigen expansion treatment.

DOI: 10.1023/A:1007460017129
Print publication date: 7/1/1998
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by Xia, L.; Becker, A.A.; Hyde, T.H.

The results of experimental creep crack growth tests, using compact tension specimens, made from a Ni-base superalloy (Waspaloy) at 700^{^}C are presented. The experimental results indicate that the creep crack growth rate data for the Ni-base superalloy Waspaloy, at 700^{^}C, can be correlated using the C^* parameter, calculated from load-line displacement rates. The mode-I stress intensity factor, K_I, does not appear to be capable of correlating the data except at high creep crack propagation rates. Analytical solutions indicate that creep crack growth was occurring under transient creep conditions in the experiments. Finite element (FE) simulations were performed in which the experimentally determined crack growth versus time results were imposed. The good agreement between the resulting FE solutions for load-line displacements and corresponding C^* values with the experimental results show that the FE simulation was successful. The FE simulation revealed that the creep zone increases as the crack growth and a transient state of creep occurs in the vicinity of the advancing crack tip. An apparent correlation between the crack growth rates and the C^* parameter has been shown. This information is helpful in assessing the likely usefulness of the C^* and K_I parameters for predicting creep crack growth in more general situations.

DOI: 10.1023/A:1007415306833
Print publication date: 7/1/1998
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by Karapetian, Edgar; Kachanov, Mark

SIFs on a circular crack due to distributed tractions are given by singular integrals over the crack surface. Surrounding the singularity point by a small (almost) semicircular region, we evaluate the singular part of the integral in a universal closed form. This leads to an accurate and numerically trivial procedure. It is also extended to moderately non-circular cracks.

DOI: 10.1023/A:1007541916027
Print publication date: 7/1/1998
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by Nuller, B.; Karapetian, E.; Kachanov, M.

Stress intensity factor (SIF) for the elliptical crack under polynomial (uniform, as a special case) loading was first given by Kassir and Sih (1975). However, their expressions contain an error, corrected by Fabrikant (1987). This correction appears to have gone largely unnoticed, and some authors still use the incorrect result.We demonstrate, on the limiting case of a very elongated crack, that the correct expression is indeed the one of Fabrikant. This is hoped to resolve the controversy. It is also pointed out how to correct other results of Kassir and Sih for various loadings.

DOI: 10.1023/A:1007534331957
Print publication date: 7/1/1998
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by Gao, X.; Ruggieri, C.; Dodds, R.H.

The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters
$$(m,\sigma _u ) $$
. Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of
$$(m,\sigma _u ) $$
provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find
$$(m,\sigma _u ) $$
which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36).

DOI: 10.1023/A:1007521530191
Print publication date: 7/1/1998
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by Giovanola, Jacques H.; Kirkpatrick, Steven W.

This paper uses a local model to predict ductile fracture in geometrically similar structures of different sizes containing either sharp cracks or blunt stress concentrators. Simple theoretical considerations suggest that when fracture occurs by quasi-isotropic void growth, fracture initiation at blunt notches follows replica scaling, whereas fracture initiation at sharp cracks does not. Simulations with a local fracture model of fracture events in (1) fatigue precracked compact specimens and (2) three-point-bend bars containing blunt notches confirm these conclusions. However, a comparison of simulations with actual experimental results with HY-130 steel specimens leads to mixed conclusions. Predicted and observed behaviors for fracture at sharp cracks agree well, but the discrepancy is considerable for fracture initiating at blunt notches loaded in bending. Significant scaling effects are observed in the experiments for the conditions of fracture initiation at blunt notches.Fractographic analysis reveals that the reason for this discrepancy is a difference in the micromechanisms controlling fracture at sharp cracks as opposed to blunt notches. At sharp cracks, quasi-isotropic void growth dominates, whereas fracture initiates at blunt notches by a shear localization process and the nucleation, growth, and coalescence of voids in a mixed shear and tensile deformation field. The transition from one mode to the other may be governed by the hardening rate and, if so, is material dependent. Therefore, when using local fracture models for predicting fracture under generalized geometric and loading conditions, care must be taken, that the micromechanisms of ductile fracture invoked in the actual material match those assumed by the local fracture model. If this correspondence is verified, local fracture models can be used to predict fracture conditions and associated scaling effects for situations not amenable to treatment by classical elasto-plastic fracture mechanics. However, new or expanded models that can treat ductile fracture in localized shear zones should be developed to realize the full potential of these local fracture methodologies.

DOI: 10.1023/A:1007573002363
Print publication date: 7/1/1998
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