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A physical model, previously developed by one of the authors, has been extended to cover thermal conductivity degradation owing to the uni-axial stress-strain response of aligned groups of fibres or tows found in ceramic matrix composites. Both the stress-strain and thermal models, together with their coupling, have been shown to predict known composite behaviour qualitatively. The degradation of longitudinal thermal properties is shown to be driven by strain-controlled fibre failure; while thedoi:10.1098/rspa.2009.0276 fatcat:lr5mil7xrneo3iibt2am6ifcua