The predictive capability of failure mode concept-based strength criteria for multi-directional laminates—part B

Abstract This contribution is a post-runner to the ‘failure exercise’. It focuses on two aspects of the theoretical prediction of failure in composites [1–3]: the first is the derivation of failure conditions for a unidirectional (UD) lamina with the prediction of initial failure of the embedded lamina, and the second the treatment of non-linear, progressive failure of 3-dimensionally stressed laminates until final failure. The failure conditions are based on the so-called Failure Mode Concept (FMC) which takes into account the material-symmetries (by the application of invariants) of the UD-lamina homogenized to a ‘material’, and on a strict failure mode thinking. The results of the investigation are stress–strain curves for the various given GFRP-/CFRP-UD-laminae, biaxial failure stress envelopes for the UD-laminae, and initial as well as final biaxial failure envelopes for the laminates. In addition a brief comparison between Puck's and Cuntze's failure theory is presented by the authors themselves.

[1]  Burton Paul,et al.  A Modification of the Coulomb-Mohr Theory of Fracture , 1961 .

[2]  Christos C. Chamis.  Probabilistic composite design , 1997 .

[3]  E. Dill,et al.  Theory of Elasticity of an Anisotropic Elastic Body , 1964 .

[4]  L. Kachanov,et al.  Foundations Of The Theory Of Plasticity , 1971 .

[5]  M. Kural,et al.  Experimental Determination of the In Situ Transverse Lamina Strength in Graphite/Epoxy Laminates , 1982 .

[6]  P. D. Soden,et al.  A further assessment of the predictive capabilities of current failure theories for composite laminates: comparison with experimental evidence , 2004 .

[7]  J. Boehler,et al.  Failure Criteria for Glass-Fiber Reinforced Composites under Confining Pressure* , 1985 .

[8]  Planar Phospholipid,et al.  RECENT ADVANCES IN , 1986 .

[9]  A. Puck.  Ein Bruckhriterium gibt die Richtung an : Weiterführende Überlegungen zum Auslegen von Faser-Kunstoff-Verbunden , 1992 .

[10]  V. Kopnov,et al.  Strength of glass-reinforced plastics in the complex stress state , 1965 .

[11]  T. A. Collings,et al.  Transverse compressive behaviour of unidirectional carbon fibre reinforced plastics , 1972 .

[12]  P. D. Soden,et al.  A COMPARISON OF THE PREDICTIVE CAPABILITIES OF CURRENT FAILURE THEORIES FOR COMPOSITE LAMINATES, JUDGED AGAINST EXPERIMENTAL EVIDENCE , 2002 .

[13]  P. D. Soden,et al.  Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: failure exercise benchmark data , 2002 .

[14]  James Martin Whitney,et al.  Theory of laminated plates , 1970 .

[15]  R. Jeltsch-Fricker.  Bruchbedingungen vom Mohrschen Typ für transversal isotrope Werkstoffe am Beispiel der Faser‐Kunststoff‐Verbunde , 1996 .

[16]  Richard M. Christensen,et al.  Yield functions/failure criteria for isotropic materials , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  P.W.M. Peters,et al.  The Strength Distribution of 90° Plies in 0/90/0 Graphite-Epoxy Laminates , 1984 .

[18]  R. Rackwitz,et al.  FORMULATIONS OF RELIABILITY-ORIENTED OPTIMIZATION , 1987 .

[19]  J. E. Bailey,et al.  On multiple transverse cracking in glass fibre epoxy cross-ply laminates , 1978 .

[20]  R. Aoki.  Verbesserung der Ausnutzbarkeit der neuen hochfesten C-Fasern in hochbelasteten Verbundstrukturen und Verbesserung des Dimensionierungsverfahrens. , 1990 .

[21]  P. D. Soden,et al.  Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates , 1998 .

[22]  H. Thom.  A review of the biaxial strength of fibre-reinforced plastics , 1998 .

[23]  V. Choo.  Effect of Loading Path on the Failure of Fibre Reinforced Composite Tubes , 1985 .

[24]  S. Meckbach,et al.  Neue Bruchkriterien und Festigkeitsnachweise für unidirektionalen Faserkunststoffverbund unter mehrachsiger Beanspruchung -Modellbildung und Experimente , 1997 .

[25]  A New Model for Inter-Fibre-Failure of High Strength Uni-Directionally Reinforced Plastics and its Reliability Implications , 1998 .

[26]  H. Awaji,et al.  A statistical theory for the fracture of brittle solids under multiaxial stresses , 1978 .

[27]  Jr Norman F. Knight,et al.  Evaluation of a Progressive Failure Analysis Methodology for Laminated Composite Structures , 1997 .

[28]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[29]  P. D. Soden,et al.  A COMPARISON OF THE PREDICTIVE CAPABILITIES OF CURRENT FAILURE THEORIES FOR COMPOSITE LAMINATES , 1998 .

[30]  Palle Thoft-Christensen,et al.  Application of Structural Systems Reliability Theory , 1986 .

[31]  H. Schürmann,et al.  FAILURE ANALYSIS OF FRP LAMINATES BY MEANS OF PHYSICALLY BASED PHENOMENOLOGICAL MODELS , 1998 .

[32]  J. Betten.  Recent advances in mathematical modelling of materials behavior , 1990 .

[33]  E. Beltrami,et al.  Sulle condizioni di resistenza dei corpi elastici , 1885 .

[34]  J. Kopp,et al.  Dimensioning of thick laminates using new IFF strength criteria and some experiments for their verification , 1996 .

[35]  J. Masters,et al.  Fractography of Modern Engineering Materials: Composites and Metals, Second Volume , 1993 .

[36]  Richard M. Christensen,et al.  The Numbers of Elastic Properties and Failure Parameters for Fiber Composites , 1998 .

[37]  L. J. Hart-Smith.  An inherent fallacy in composite interaction failure curves , 1993 .

[38]  R. Christensen.  Stress based yield/failure criteria for fiber composites , 1997 .

[39]  Robert L. Taylor,et al.  A constitutive model for anisotropic damage in fiber-composites , 1995 .

[40]  Z. Hashin.  Failure Criteria for Unidirectional Fiber Composites , 1980 .