In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1 Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations A mixed boundary value problem from the theory of elasticity is considered as an example Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

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On the solution of integral equations with strong ly singular kernels

http://www.jmcx.utad.pt/pdf/Koerber2010_High%20strain%20rate%20characterisation%20of%20unidirectional%20carbon-epoxy%20IM7-8552%20in%20transverse%20compression%20and%20in-plane%20shear%20using%20DIC.pdf

High strain rate characterisation of unidirectional carbon-epoxy IM7-8552 in transverse compression and in-plane shear using digital image correlation

Stress Intensity Fctor for Intermal and Extemal Surface Cracks in Cylindrical Vessels

Tension behavior of unidirectional glass/epoxy composites under different strain rates

Strain-rate-dependent failure criteria for composites

Methods for dynamic characterization of composite materials were extended and applied to the study of strain rate effects under transverse compression as well as shear. Falling weight impact and Split Hopkinson Pressure Bar systems were developed for dynamic characterization of composite materials in compression and shear at strain rates up to 1800 sO. Strain rates below 10 s5l were generated using a servohydraulic testing machine. Strain rates between 10 sol and 300 sol were generated using the drop tower apparatus. Strain rates above 500 s-l were generated using the Split Hopkinson Pressure Bar.Seventy-two and forty-eight ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the transverse direction were characterized. Off-axis (15°, 300, 450 and 600) compression tests of the same unidirectional material were also conducted to obtain the in-plane shear stress-strain behavior. Strain rates over a wide range, from 10-4 s-1 (quasi-static) up to 1800 s-1, were recorded. The 90-degree properties,...

Strain Rate Effects on the Transverse Compressive and Shear Behavior of Unidirectional Composites

The effect of strain rate on the compressive behavior of thick carbon/epoxy composite materials was investigated. Falling weight impact and split Hopkinson pressure bar systems were developed for dynamic characterization of composite materials in compression at strain rates up to 2000 s−1. Strain rates below 10 s−1 were generated using a servohydraulic testing machine. Strain rates between 10 s−1 and 500 s−1 were generated using the drop tower apparatus. Strain rates above 500 s−1 were generated using the split Hopkinson pressure bar. Unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions, and\([(0_8 /90_8 )_2 /\bar 0_8 ]_s \) cross-ply laminates were characterized. The 90-deg properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The 0-deg and cross-ply laminates show higher strength and ultimte strain values as the strain rate increases, whereas the modulus increnases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases, the dynamic stress-strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal direction and highest in the transverse direction.

R. D. Cordes

Papers

Strain Rate Effects on the Transverse Compressive and Shear Behavior of Unidirectional Composites

Dynamic compressive behavior of thick composite materials

Dynamic response of carbon/epoxy composites

Determination of interfacial properties from observations of progressive fiber debonding and pullout

Surface Cracks in Toroidal Shells