Journal of the European Ceramic Society 15(1995) Printed in Great Britain. All right 09552219(95)00095 Toughness of Damage Tolerant Continuous Fibre Reinforced Ceramic Matrix Composites Bent F. Sorensen@& Ramesh talreja Materials Departrnent, Rise National Laboratory, 4000 Roskilde, Denmark sChool of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA (Received 30 March 1995; revised version received 24 May 1995; accepted 25 May 1995) abstract I potential energy g stress A simple shear-lag model is used to estimate the Ts interfacial sliding shear stress toughness of a unidirectional fibre reinfored ceramic strain energy density matrix composite. In the model, which includes the residual axial stresses, the stress transfer across Subscript fibre/matrix interface is by a constant shear stress. db debonding estimates from the model experimental measurements for four composites and m matrix good agreement is found. The effects uf distributed mux value at specimen separation and localized energy uptake on fracture stability are mc matrix cracking discussed, and it is concluded that for most appli- u value at ultimate tions the toughness, rather than the pull-out energy Fs full sliding along the interface absorption, should be maximized. Superscript ACK fully and multiply cracked matrix Nomenclature ini initiation of matrix cracks fibre radius value after specimen separation a cross-section area Initial state B specimen width I-IV stages of damage crack length e Young' s modulus f fibre volume fraction 1 Introduction G (critical) energy-release-rate L Monolithic ceramics are brittle, flaw-sensitive and of s sliding length low energy absorption capacity before and during P pull-out length fracture. However, a class of ceramic composites applied load with continuous reinforcement is emerging, which s spacing of m cracks has much more attractive damage and fracture toughness(ene r unit volume) of com- behaviour. Materials in this class are damage toler- ant,in the sense that the first mode of damage displacement (matrix cracking) does not lead to final fracture W energy dissipated(per unit volume) due to Instead, the strength of the materials is controlled frictional sliding by the strength of the reinforcement. This flaw energy dissipated (per unit area) due to fibre insensitive behaviour is a remarkable property of materials that are made of brittle constituents. As ywoF work of fracture a consequence, fracture toughness is not a proper 8 matrix crack opening parameter to characterize such materials. Rather, 4 specimen elongation the stress at the onset of multiple matrix cracking, axial strain the failure stress, and total energy ' uptake until eu ultimate tensile strain failure constitute a set of property parametersJournal of the European Ceramic Sociery 15 (1995) 1047-1059 0 1995 Elsevier Science Limited 0955-2219(95)00095-X Printed in Great Britain. All rights reserved 0955-2219/95/$9.50 Toughness of Damage Tolerant Continuous Fibre Reinforced Ceramic Matrix Composites Bent F. SOrensena 1E Ramesh Talrejab “Materials Department, Riser National Laboratory, 4000 Roskilde, Denmark ‘School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA (Received 30 March 1995; revised version received 24 May 1995; accepted 25 May 1995) Abstract A simple shear-lag model is used to estimate the toughness of a unidirectionaljbre reinfored ceramic matrix composite. In the model, which includes the residual axial stresses, the stress transfer across the jibre/matrix interface is by a constant shear stress. The estimates from the model are compared to experimental measurements for four composites and good agreement is found. The efsects of distributed and localized energy uptake on fracture stability are discussed, and it is concluded that for most appli￾cations the toughness, rather than the pull-out energy absorption, should be ma.ximized. Nomenclature B ; f G L 1, 1P P S u V Ki w, %/OF s A E eu fibre radius cross-section area specimen width crack length Young’s modulus fibre volume fraction (critical) energy-re:lease-rate specimen length sliding length pull-out length applied load spacing of matrix cracks toughness (energy per unit volume) of com￾posite displacement energy dissipated (per unit volume) due to frictional sliding energy dissipated ‘(per unit area) due to fibre pull out work of fracture matrix crack open.ing specimen elongation axial strain ultimate tensile strain IT potential energy (T stress 7s interfacial sliding shear stress 4 strain energy density Subscript db debonding f fibre m matrix max value at specimen separation mc matrix cracking U value at ultimate stress FS full sliding along the interface Superscript ACK ini res * 0 I-IV fully and multiply cracked matrix initiation of matrix cracks residual value after specimen separation initial state stages of damage 1 Introduction Monolithic ceramics are brittle, flaw-sensitive, and of low energy absorption capacity before and during fracture. However, a class of ceramic composites with continuous reinforcement is emerging, which has much more attractive damage and fracture behaviour. Materials in this class are damage toler￾ant, in the sense that the first mode of damage (matrix cracking) does not lead to final fracture. Instead, the strength of the materials is controlled by the strength of the reinforcement. This flaw￾insensitive behaviour is a remarkable property of materials that are made of brittle constituents. As a consequence, fracture toughness is not a proper parameter to characterize such materials. Rather, the stress at the onset of multiple matrix cracking, the failure stress, and total energy ‘uptake until failure constitute a set of property parameters. 1047