A statistical theory for the fracture of brittle solids under multiaxial stresses
01 Feb 1978-International Journal of Fracture (Springer Science and Business Media LLC)-Vol. 14, Iss: 1
About: This article is published in International Journal of Fracture.The article was published on 1978-02-01. It has received 17 citations till now. The article focuses on the topics: Fracture (geology).
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TL;DR: In this paper, the failure conditions for a unidirectional lamina are derived based on the Failure Mode Concept (FMC) which takes into account the material-symmetries (by the application of invariants) of the UD-lamina homogenized to a material, and on a strict failure mode thinking.
238 citations
TL;DR: In this article, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test.
36 citations
Cites methods from "A statistical theory for the fractu..."
...Linear elastic fracture mechanics has been used to assess the fracture resistance of graphite specimens [12-15]....
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TL;DR: The failure mode concept model was used in the second world-wide failure exercise as discussed by the authors, which dealt with the behaviour of isotropic material and unidirectional as well as multidirectal unIDirectional laminae-composed laminates subjected to three dimensional (triaxial) states of stress.
Abstract: This paper represents the author’s contribution to the second world-wide failure exercise using his failure mode concept modelling capability. The second world-wide failure exercise deals with the behaviour of isotropic material and unidirectional as well as multidirectional unidirectional laminae-composed laminates subjected to three-dimensional (triaxial) states of stress. Twelve challenging test cases were provided by the organisers and those covered stress–strain curves and failure envelopes under three-dimensional stress states. The application of the new failure mode concept model has extended the three-dimensional modelling by taking into account the effects of hydrostatic pressure and second glass temperature shift factor on the stress–strain curves and failure envelopes. The failure mode concept model was capable of successfully solving the majority of all the problems and a comparison between the predictions and test data is planned to be published in Part B of the second world-wide failure exer...
34 citations
TL;DR: In this paper, an infrared radiation (IR) heating method was used to evaluate thermal shock parameters (thermal shock strength and thermal shock fracture toughness) of float glass and alumina.
Abstract: An infrared radiation(IR) heating method was used to evaluate thermal shock parameters(thermal shock strength and thermal shock fracture toughness)of float glass and alumina. This technique makes it possible to evaluate the parameters directly from the electric power of the IR heater. In this paper we discuss how the pertinent thermal shock parameters should be estimated both as physical properties of a material and as a function of temperature. The stress intensity factors for a disk with an edge crack were analyzed numerically under a thermal shock loading. The thermal shock parameters in both ambient and elevated-temperature environments were measured by the IR heating technique and the results were compared with predicted values, which combined such emperature-dependent properties of the material as Young's modulus, thermal conductivity, linear thermal expansion, and tensile strength or fracture toughness.
22 citations
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TL;DR: In this article, the applicability of statistics to a wide field of problems is discussed, and examples of simple and complex distributions are given, as well as a discussion of the application of statistics in a wide range of problems.
Abstract: This paper discusses the applicability of statistics to a wide field of problems. Examples of simple and complex distributions are given.
9,091 citations
TL;DR: In this paper, a weakest link theory for macroscopically homogeneous isotropic materials containing uniformly distributed, randomly oriented cracks is developed under the assumption that fracture depends only on the stress normal to a crack plane.
Abstract: : A weakest link theory for macroscopically homogeneous isotropic materials containing uniformly distributed, randomly oriented cracks is developed under the assumption that fracture depends only on the stress normal to a crack plane. The function representing the number of cracks failing at each value of normal stress is expanded as a Taylor series with coefficients determined from tensile test data. This function is used without additional assumptions to determine the probability of fracture under arbitrary stress conditions. The results can be readily incorporated into a finite element code to predict the failure probability of any structure to which the code applies. (Author)
303 citations
TL;DR: In this paper, the authors show that the assumption that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually is generally unconservative and therefore the approximation serves as a lower bound to the failure probability.
Abstract: A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple technique is given for finding an upper bound in cases of biaxial tension provided the uniaxial fracture behavior is described satisfactorily by Weibull's two-parameter formula. The upper bound is a good approximation when in high stress regions the stresses are equibiaxial, or nearly so, as in laterally loaded or spinning disks.
57 citations
16 citations