Hashin Failure Criteria

Department Department of Aerospace Engineering Engineering Indian Institute of Technology Kanpur AE 681 Composite Materials Hashin’s Failure Criteria for Unidirectional Unidirectional Fibre Composites These are interacting failure criteria where more than one stress components have  been used to evaluate evaluate the different different failure modes. These criteria criteria were originally developed developed for unidirectional polymeric composites, and hence, applications to other type of laminates and non-polymeric composites have significant approximations. Usually Hashin criteria are implem implemente ented d within within two dimensi dimensional onal classi classical cal laminat lamination ion approac approach h for point point stress stress calculations with ply discounting as the material degradation model. Failure indices for  Hashin criteria are related to fibre and matrix failures and involve four failure modes. The criteria criteria are extended to three dimensional dimensional problems problems where the maximum stress criteria criteria are used for transverse normal stress component. The failure modes included in Hashin’s criteria are as follows. 1. Tensi Tensile le fib fibre re fai failu lure re for for σ11 ≥ 0 2

 σ  11   σ 122 + σ  123  ≥ 1   X   + S 2 = < 1  12    T 

failure no failure

2. Comp Compre ress ssive ive fibr fibree fail failur uree for σ11 < 0 2

 σ  11    ≥ 1   X    = < 1     C 

failure no failure

3. Tensi Tensile le mat matri rix x fail failure ure for σ22 + σ33 > 0

( σ 22 + σ  33 ) 2

YT 

2

+

σ

2 23

− σ 22σ  33 2

S 23

+

2 σ 12

+ σ  2

13

2

S 12

≥1 = < 1

failure no failure

4. Compre Compressi ssive ve matr matrix ix fail failure ure for σ22 + σ33 < 0

 Y  2   σ 22 + σ 33  (  σ 22 + σ  33 ) 2 σ 223 − σ 22σ 33   σ 122   + σ  2  ≥ 1  − 1  + + =   +   4S 2 2 2 2 S23 S12   < 1  S23    Y 23    C 

13

C 

Department Department of Aerospace Engineering, Indian Institute of Technology Technology Kanpur  Course: AE 681 Composite Materials Materials Instructor: PM Mohite

failure no failure

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5. Interl Interlami aminar nar tensil tensilee failu failure re for σ33 > 0 2

 σ  33     Z       T 

≥1 = < 1

failure no failure

6. Interl Interlami aminar nar comp compres ressio sion n failur failuree for σ33 < 0 2

 σ  33    ≥ 1   Z    = < 1     C 

failure no failure

where, σij denote the stress components and the tensile and compressive allowable strengths for lamina lamina are denoted denoted by subscr subscript iptss T  and C , respect respectivel ively. y. XT, YT, ZT denotes denotes the allowable tensile strengths in three respective material directions. Similarly, X C, YC, ZC denotes the allowable allowable tensile strengths in three respective respective material material directions. Further, S12, S13 and S23 denote allowable shear strengths in the respective principal material directions.

Reference: Hashin Z. Failure criteria for unidirectional fibre composites, ASME Journal of Applied Mechanics, Vol. 47 (2), 1980, pp 329-334.

Department Department of Aerospace Engineering, Indian Institute of Technology Technology Kanpur  Course: AE 681 Composite Materials Materials Instructor: PM Mohite

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