TABLE 2.1 Basic Strengths of Orthotropic Plies for Plane Stress Direction/Plane Active Stress Strength Ultimate Strain 1 G1 XI.X. ef,ef 2 02 X3X ez.es 12 112 S es Note:All strengths and ultimate strains are defined by their magnitudes. fibers is independent of the sign of the shear stress.The presentation is limited to plane stress in the plane of the fibers.Table 2.1 lists the five independent failure stresses and strains corresponding to plane stress. Notice here that superscripts T and C denote tension and compression, respectively,and that strengths and ultimate strains are defined as positive, i.e.,the symbols indicate their magnitudes.For example,a composite ply loaded in pure negative shear(t2<0)would fail at a shear stress t12=-S6 and shear strain Y2 =-e6. 2.5.1 Maximum Stress Failure Criterion The maximum stress failure criterion assumes that failure occurs when any one of the in-plane stresses o,02,or tattains its limiting value independent of the other components of stress.If the magnitudes of the stress components are less than their values at failure,failure does not occur,and the element or structure is considered safe.For determining the failure load,any of the following equalities must be satisfied at the point when failure occurs: 01=X (2.42a) 01=-X9 (2.42b) 02=X (2.42c) 02=-X9 (2.42d) T12=S6 (2.42e) T2=-S6 (2.420 For unidirectional and fabric composites,Equations(2.42a and b)indicate failure of fibers at quite high magnitudes of stress,whereas Equations(2.4c-f) indicate matrix or fiber-matrix interface dominated failures at much lower ©2003 by CRC Press LLCfibers is independent of the sign of the shear stress. The presentation is limited to plane stress in the plane of the fibers. Table 2.1 lists the five independent failure stresses and strains corresponding to plane stress. Notice here that superscripts T and C denote tension and compression, respectively, and that strengths and ultimate strains are defined as positive, i.e., the symbols indicate their magnitudes. For example, a composite ply loaded in pure negative shear (τ12 < 0) would fail at a shear stress τ12 = –S6 and shear strain γ12 = – e6. 2.5.1 Maximum Stress Failure Criterion The maximum stress failure criterion assumes that failure occurs when any one of the in-plane stresses σ1, σ2, or τ12 attains its limiting value independent of the other components of stress. If the magnitudes of the stress components are less than their values at failure, failure does not occur, and the element or structure is considered safe. For determining the failure load, any of the following equalities must be satisfied at the point when failure occurs: (2.42a) (2.42b) (2.42c) (2.42d) τ12 = S6 (2.42e) τ12 = –S6 (2.42f) For unidirectional and fabric composites, Equations (2.42a and b) indicate failure of fibers at quite high magnitudes of stress, whereas Equations (2.4c–f) indicate matrix or fiber–matrix interface dominated failures at much lower TABLE 2.1 Basic Strengths of Orthotropic Plies for Plane Stress Direction/Plane Active Stress Strength Ultimate Strain 1 σ1 2 σ2 1,2 τ12 S6 e6 Note: All strengths and ultimate strains are defined by their magnitudes. X X T C 1 1 , e e T C 1 1 , X X T C 2 2 , e e T C 2 2 , σ1 1 = XT σ1 1 = −XC σ2 2 = XT σ2 2 = −XC TX001_ch02_Frame Page 25 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC