Hashin Failure Criteria
2
Department of Aerospace Engineering, Indian Institute of Technology Kanpur Course: AE 681 Composite Materials Instructor: PM Mohite 1 Department of Aerospace Engineering Indian Institute of Technology Kanpur AE 681 Composite Materials Hashin’s Failure Criteria for Unidirectional Fibre Composites These are interacting failure criteria where more than one stress components have been used to evaluate the different failure modes. These criteria were originally developed for unidirectional polymeric composites, and hence, applications to other type of laminates and non-polymeric composites have significant approximations. Usually Hashin criteria are implemented within two dimensional classical lamination approaches for point 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 are extended to three dimensional problems where the maximum stress criteria are used for transverse normal stress component. The failure modes included in Hashin’s criteria are as follows. 1. Tensile fibre failure for σ 11 ≥ 0 2 2 2 12 13 11 2 12 1 failure 1 no failure T X S 2. Compressive fibre failure for σ 11 < 0 2 11 1 failure 1 no failure C X 3. Tensile matrix failure for σ 22 + σ 33 > 0 13 2 2 2 2 12 22 33 23 22 33 2 2 2 23 12 1 failure 1 no failure T Y S S 4. Compressive matrix failure for σ 22 + σ 33 < 0 13 2 2 2 2 2 12 22 33 22 33 23 22 33 2 2 2 23 23 23 12 1 failure 1 1 no failure 2 4 C C Y S Y S S S
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Failure criteria for composite materials. Out of the several possible criteria to design failure, Hashin is one important amongst the lot and is discussed in here
Transcript of Hashin Failure Criteria
Department of Aerospace Engineering, Indian Institute of Technology Kanpur
Course: AE 681 Composite Materials
Instructor: PM Mohite
1
Department of Aerospace Engineering
Indian Institute of Technology Kanpur
AE 681 Composite Materials
Hashin’s Failure Criteria for Unidirectional Fibre Composites
These are interacting failure criteria where more than one stress components have
been used to evaluate the different failure modes. These criteria were originally
developed for unidirectional polymeric composites, and hence, applications to other type
of laminates and non-polymeric composites have significant approximations. Usually
Hashin criteria are implemented within two dimensional classical lamination approaches
for point 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 are extended to three dimensional problems where the
maximum stress criteria are used for transverse normal stress component.
The failure modes included in Hashin’s criteria are as follows.
1. Tensile fibre failure for σ11 ≥ 0
2
2 2
12 1311
2
12
1 failure
1 no failureTX S
2. Compressive fibre failure for σ11 < 0
2
111 failure
1 no failureCX
3. Tensile matrix failure for σ22 + σ33 > 0
13
2 2 221222 33 23 22 33
2 2 2
23 12
1 failure
1 no failureTY S S
4. Compressive matrix failure for σ22 + σ33 < 0
13
2 2 2 221222 3322 33 23 22 33
2 2 2
23 23 23 12
1 failure 1
1 no failure2 4
C
C
Y
S Y S S S
Department of Aerospace Engineering, Indian Institute of Technology Kanpur
Course: AE 681 Composite Materials
Instructor: PM Mohite
2
5. Interlaminar tensile failure for σ33 > 0
2
331 failure
1 no failureTZ
6. Interlaminar compression failure for σ33 < 0
2
331 failure
1 no failureCZ
where, σij denote the stress components and the tensile and compressive allowable
strengths for lamina are denoted by subscripts T and C, respectively. XT, YT, ZT denotes
the allowable tensile strengths in three respective material directions. Similarly, XC, YC,
ZC denotes the allowable tensile strengths in three respective 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.
