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Keywords: composite, fatigue, damage mechanics, finite element analysis, stiffness.

Summary

Fibre-reinforced composites are used in many fatigue-critical applications, but their fatigue behaviour is complex and knowledge is far from complete. The fatigue models for fibre-reinforced composites can generally be classified into: (i) fatigue life models (S-N curves), (ii) phenomenological residual stiffness/residual strength models, and (iii) damage accumulation models (`mechanistic models'). The presently proposed fatigue model is based on the residual stiffness approach, because this approach allows for modelling stiffness degradation, stress redistribution and accumulation of permanent strain; each of these phenomena being observed in the performed fatigue tests.

Indeed, experimental results were obtained from displacement-controlled bending fatigue tests on plain woven glass/epoxy composites. The specimens were clamped at the upper end and the displacement was prescribed at the lower end (cantilever beam loading). Eight layers of fabric were stacked in two sequences: (i) under 0^o with the bending direction ([#0^o]₈), and (ii) under 45^o ([#0^o]₈). Due to the (bending) stiffness degradation, the necessary force to bend the specimen, decreased during fatigue life. Further, it was observed that the out-of-plane bending profile of the [#0^o]₈ specimens drastically changed during loading time from a smoothly curved profile at the first loading cycles, to a straight profile with a sort of `hinge' at the clamped cross-section. On the other hand, the bending profile of the [#45^o]₈ specimens remained unchanged during the whole loading time, but these specimens showed a considerable permanent deformation after unloading (about 18% of the prescribed displacement at the lower specimen end). Summarized, in order to simulate these phenomena, the model should be able to simulate: (i) stiffness degradation (decreasing bending force), (ii) stress redistribution (changing bending profiles), and (iii) accumulation of permanent strain.

To that purpose, a residual stiffness model was developed with three damage variables: $D_{11}$ (damage in the $\vec{e}_{11}$ direction), $D_{22}$ (damage in the $\vec{e}_{22}$ direction), and $D_{12}$ (shear damage). These damage variables are directly related with the corresponding stress components $\sigma_{11}$ (positive/negative), $\sigma_{22}$ (positive/negative) and $\sigma_{12}$ in the orthotropic directions of the glass/epoxy composite. For each of the three damage variables, the growth rate per fatigue cycle is defined by a differential equation d $(D_{ij})/$ d. To make a prediction of the moment of failure, the governing stresses $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ in the corresponding differential equations have been replaced by the newly defined fatigue failure indices $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ . These failure indices are calculated from the Tsai-Wu static failure criterion, where the nominal stresses $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ are replaced by the effective stresses $\tilde{\sigma}_{11}$ , $\tilde{\sigma}_{22}$ and $\tilde{\sigma}_{12}$ . As such, there is a correlation with residual strength, and the moment of failure in the displacement-controlled bending fatigue tests can be predicted as well.

Finally, the permanent strains $\varepsilon_{ii}^p$ (i=1,2) have been introduced. The growth rate d $(\varepsilon_{ii}^p)/$ d is proportional with the elastic strain $\varepsilon_{ii}$ and the growth rate d $(D_{12})/$ d.

All constitutive equations have been implemented in the commercial finite element code SAMCEF^TM. The composite specimen has been modelled with isoparametric solid brick elements, one element through the thickness for each of the eight composite plies. Further the clamping plates at the fixation and the displacement mechanism at the lower specimen end have been included in the finite element mesh. It has been shown that the correct modelling of the boundary conditions is extremely important to yield reliable results.

The whole fatigue life from the first loading cycle up to final failure is simulated, and stiffness degradation, stress redistribution, and accumulation of permanent strain are accounted for. As it is impossible to simulate each individual fatigue loading cycle, an adaptive time stepping algorithm has been implemented. The algorithm evaluates how many cycles can be jumped over without losing accuracy on the evolution and growth of damage in all integration points of the finite element mesh. It is assumed that the damage increments d $(D_{ij})/$ d are constant during these cycle jumps.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 77 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping Paper 98 Simulating Damage and Permanent Strain in Composites under In-Plane Fatigue Loading W. Van Paepegem and J. Degrieck Department of Mechanical Construction and Production, Ghent University, Gent, Belgium doi:10.4203/ccp.77.98 purchase the full-text of this paper Full Bibliographic Reference for this paper W. Van Paepegem, J. Degrieck, "Simulating Damage and Permanent Strain in Composites under In-Plane Fatigue Loading", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2003. doi:10.4203/ccp.77.98 Keywords: composite, fatigue, damage mechanics, finite element analysis, stiffness. Summary Fibre-reinforced composites are used in many fatigue-critical applications, but their fatigue behaviour is complex and knowledge is far from complete. The fatigue models for fibre-reinforced composites can generally be classified into: (i) fatigue life models (S-N curves), (ii) phenomenological residual stiffness/residual strength models, and (iii) damage accumulation models (`mechanistic models'). The presently proposed fatigue model is based on the residual stiffness approach, because this approach allows for modelling stiffness degradation, stress redistribution and accumulation of permanent strain; each of these phenomena being observed in the performed fatigue tests. Indeed, experimental results were obtained from displacement-controlled bending fatigue tests on plain woven glass/epoxy composites. The specimens were clamped at the upper end and the displacement was prescribed at the lower end (cantilever beam loading). Eight layers of fabric were stacked in two sequences: (i) under 0^o with the bending direction ([#0^o]₈), and (ii) under 45^o ([#0^o]₈). Due to the (bending) stiffness degradation, the necessary force to bend the specimen, decreased during fatigue life. Further, it was observed that the out-of-plane bending profile of the [#0^o]₈ specimens drastically changed during loading time from a smoothly curved profile at the first loading cycles, to a straight profile with a sort of `hinge' at the clamped cross-section. On the other hand, the bending profile of the [#45^o]₈ specimens remained unchanged during the whole loading time, but these specimens showed a considerable permanent deformation after unloading (about 18% of the prescribed displacement at the lower specimen end). Summarized, in order to simulate these phenomena, the model should be able to simulate: (i) stiffness degradation (decreasing bending force), (ii) stress redistribution (changing bending profiles), and (iii) accumulation of permanent strain. To that purpose, a residual stiffness model was developed with three damage variables: $D_{11}$ (damage in the $\vec{e}_{11}$ direction), $D_{22}$ (damage in the $\vec{e}_{22}$ direction), and $D_{12}$ (shear damage). These damage variables are directly related with the corresponding stress components $\sigma_{11}$ (positive/negative), $\sigma_{22}$ (positive/negative) and $\sigma_{12}$ in the orthotropic directions of the glass/epoxy composite. For each of the three damage variables, the growth rate per fatigue cycle is defined by a differential equation d $(D_{ij})/$ d. To make a prediction of the moment of failure, the governing stresses $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ in the corresponding differential equations have been replaced by the newly defined fatigue failure indices $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ . These failure indices are calculated from the Tsai-Wu static failure criterion, where the nominal stresses $\sigma_{11}$ , $\sigma_{22}$ and $\sigma_{12}$ are replaced by the effective stresses $\tilde{\sigma}_{11}$ , $\tilde{\sigma}_{22}$ and $\tilde{\sigma}_{12}$ . As such, there is a correlation with residual strength, and the moment of failure in the displacement-controlled bending fatigue tests can be predicted as well. Finally, the permanent strains $\varepsilon_{ii}^p$ (i=1,2) have been introduced. The growth rate d $(\varepsilon_{ii}^p)/$ d is proportional with the elastic strain $\varepsilon_{ii}$ and the growth rate d $(D_{12})/$ d. All constitutive equations have been implemented in the commercial finite element code SAMCEF^TM. The composite specimen has been modelled with isoparametric solid brick elements, one element through the thickness for each of the eight composite plies. Further the clamping plates at the fixation and the displacement mechanism at the lower specimen end have been included in the finite element mesh. It has been shown that the correct modelling of the boundary conditions is extremely important to yield reliable results. The whole fatigue life from the first loading cycle up to final failure is simulated, and stiffness degradation, stress redistribution, and accumulation of permanent strain are accounted for. As it is impossible to simulate each individual fatigue loading cycle, an adaptive time stepping algorithm has been implemented. The algorithm evaluates how many cycles can be jumped over without losing accuracy on the evolution and growth of damage in all integration points of the finite element mesh. It is assumed that the damage increments d $(D_{ij})/$ d are constant during these cycle jumps. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £123 +P&P)
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