II.1.10 Failure theories

When stresses and strains have been calculated in plies (or some of the plies), the failure indices can be estimated too. One presents below the different failure theories that are proposed in FeResPost, and how these failure theories can be used to estimate laminate reserve factors.

In this section, one conventionally uses integer subscripts to denote that tensor components are given in ply axes and Roman subscripts to indicate principal components. Often, only in-plane components of ply stress or strain tensors are used to estimate criteria. Then, the principal components are estimated as follows:

In the rest of this section all the allowables used in failure criteria have positive values. Even the compressive allowables are $\ge 0$.

Table II.1.2 summarizes the criteria available in FeResPost. For each criterion, the Table provides:

1.

A String corresponding to the argument that identifies the selected criterion when derivation is asked.

2.

A description of the type of material (metallic or isotropic, unidirectional tape, fabric,...).

3.

A reference to the section in which the criterion is presented and discussed.

4.

Specification whether an equivalent stress for this criterion can be derived in FeResPost or not.

5.

One specifies whether a failure index can be derived with FeResPost. Generally, the failure index is calculated according to the “usual” definition in litterature. when no such standard failure index definition is available, one provides a default definition which corresponds to the inverse of the reserve factor calculated with $FoS=1$.

6.

One specifies whether a reserve factor and/or strength ratio can be calculated with FeResPost:

• The “reserve factor” (RF) can be defined as the factor by which laminate loads can be multiplied to reach the threshold of composite failure according to the selected failure criterion. A safety factor is included in the calculation of reserve factor.
• The “strength ratio” (SR) is defined as the inverse of the reserve factor. Here again; the factor of safety is taken into account for the calculation of strength ratio.

Note that many of the criteria presented here are particular cases of a general quadratic criterion that requires first the calculation of a failure index:

then a test is done on the calculated value:

This means that no failure occurs if $f\le 1$ (ply or laminate passes the failure test) and one has failure if $f>1$.

Several failure theories discussed below are obtained by expressing the coefficients in the expressions above by expressions depending on the material allowables. Also for the Tsai-Wu criteria discussed in section II.1.10.14 and II.1.10.15, the parameters $F_{ij}$ are directly characterized for the material.

Note that the 2D criteria defined in this section often correspond to the failure criteria defined in ESAComp.