A General Theory of Strength for Anisotropic Materials
01 Jan 1971-Journal of Composite Materials (Sage PublicationsSage CA: Thousand Oaks, CA)-Vol. 5, Iss: 1, pp 58-80
TL;DR: In this article, an operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors, which satisfies the invariant requirements of coordinate transforma tion, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses.
Abstract: An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.
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TL;DR: In this paper, the authors review the analysis of composite materials from the applied mechanics and engineering science point of view, including elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity, static strength, and fatigue failure.
Abstract: The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.
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TL;DR: In this paper, a simple fatigue failure criterion for unidirectionally fiber reinforced laminae under oscillatory states of combined plane stress has been presented, expressed in terms of thre
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Cites methods from "A General Theory of Strength for An..."
...In addition, theoretical formulations have been proposed (80, 81) based on the Tsai-Wu quadratic theory, which was originally developed for engineering composite materials (82, 83), and on cellular solid theory (79)....
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TL;DR: In this article, a 3D failure criteria for laminated fiber-reinforced composites, based on a physical model for each failure mode and considering non-linear matrix shear behavior, are developed.
Abstract: 3D failure criteria for laminated fibre-reinforced composites, based on a physical model for each failure mode and considering non-linear matrix shear behaviour, are developed. Special emphasis is given to compression failure. The physical model for matrix compression failure is based on the Mohr–Coulomb criterion and also predicts the fracture angle. For fibre kinking, an initial fibre-misalignment angle is considered to trigger failure, due to further rotation during the compressive loading. The plane where the kinking takes place is predicted by the model, as well as the kink-band angle. Applications are presented that validate the model against experimental data.
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Cites background from "A General Theory of Strength for An..."
...Tsai and Wu [134] expressed this criterion in terms of the stress tensor and two material dependent tensors....
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...The Tsai–Wu quadratic criterion [134] is an obvious candidate for a multiaxial anisotropic failure criterion since it accounts for strength asymmetry (different tensile and compressive strengths) and anisotropy, as well as interactions between strengths under different loading conditions....
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References
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Book•
01 Jan 1950
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy
7,810 citations
TL;DR: In this article, a phenomenological fracture condition for ortho tropic brittle materials is proposed, which can account for widely differing compressive and tensile strengths in ortho tropical brittle materials.
Abstract: A phenomenological fracture condition is proposed for ortho tropic brittle materials. It contains nine material parameters and can account for widely differing compressive and tensile strengths in ...
694 citations
"A General Theory of Strength for An..." refers methods in this paper
...For the graphite-epoxy composite presented in this paper, the quadratic approximation of the strength criterion proposed by Hoffman [10], which is an improvement over Hill’s [2] by incorporating the effect of internal stresses, has an interaction term so small ( -....
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01 Mar 1968
TL;DR: The use of these invariants in materials evaluation and design optimization is discussed in this article, where simple formulas, based upon micromechanics results, are derived for the invariant in terms of constituent material properties.
Abstract: : Invariant properties of the elastic coefficient matrices of laminated composite plates are presented. The use of these invariants in materials evaluation and design optimization is discussed. Simple formulas, based upon micromechanics results, are derived for the invariants in terms of constituent material properties. (Author)
271 citations
"A General Theory of Strength for An..." refers methods in this paper
...In particular, the transformation relations in terms of multiple angles, similar to those developed for the elastic stiffness [3], are useful tools for the understanding of strength tensors....
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TL;DR: In this paper, a tensor invariant strength criterion for anisotropic materials of the glass-reinforced plastic type is proposed, which takes into account not only the different ultimate strengths in tension and compression in each direction but also the dependence of the ultimate shear strengths on the sign (direction) of the shear stresses.
Abstract: A new criterion of strength is proposed for anisotropic materials of the glass-reinforced plastic type. This criterion takes into account not only the different ultimate strengths in tension and compression in each direction but also the dependence of the ultimate shear strengths on the sign (direction) of the shear stresses. The criterion is given in tensor invariant form, so that it can be rewritten for any direction of the glass fibers. The criteria proposed by other authors, in particular, R. Hill's condition of plasticity [1], follow from the new generalized criterion as special cases. The results of experiments conducted both by the authors of the present article and by other investigators provide good confirmation of the proposed criterion.
127 citations
"A General Theory of Strength for An..." refers background or methods in this paper
...This was shown by Ashkenazi [8] when he substituted an unconstrained value for F12 into the theory proposed by Gol’denblat and Kopnov [4]....
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...(7) Finally, Gol’denblat and Kopnov [4] was one of the first to suggest the use of strength tensors and proposed a general theory in the following form:...
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...The Russian workers [4, 8] suggested the use of off-axis tests, with the 45-degrce specimen...
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TL;DR: In this paper, a modification of Marin's criterion that includes six constants, five of which are evaluated from four uniaxial loading conditions and a pure shear condition, is introduced.
33 citations
"A General Theory of Strength for An..." refers background in this paper
...Some authors have tried to generalize the quadratic approximation derived from Equation (35b) by introducing floating or adjustable constants for the off-diagonal or interaction terms such as [7] ]...
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