In order to determine the strength reserves of a laminate, one must proceed in layers.
Starting off with calculating the effective stress per layer, an evaluation of these states of stress consequently follows in order to identify and eventually re-dimension the strength reserves. The mechanical load leads to a variety of stress states within the respective layers, which are analyzed utilizing a strength criterion. The criterion is needed due to the fact, that the strength of a single layer cannot be determined experimentally for all possible stress combinations.
Stress calculation according to classical laminate theory
The classical laminate theory (CLT) is used for the calculation of laminate stress and forming resulting from external loads and momenta. CLT is based on the presumptions according to Kirchhoff’s plate theory, thus limited to calculating plain stresses.
Linear and non-linear Strength calculation
A description of the fracture event of a lamina in a laminate is rendered more difficult not only by its anisotropy but also by the occurrence of two types of fracture which are fundamentally different in their forms and effects, namely FF and IFF. Furthermore, the fracture analysis of the laminate becomes more complicated due to two more effects.
1. The different laminas in a laminate do not normally reach their fracture limits simultaneously. Some laminae in a laminate may be loaded up to the IFF limit or have even already exceeded the limit, while others are still a long way from a fracture limit. As a consequence, the stress state in the different laminas changes due to IFF.
2. In addition, under certain loading conditions the distribution of loads over the individual laminae of the laminate will vary as a function of the stress level – this is due to the nonlinear stress-strain interrelationships.
Non-linear stress analysis before IFF
The shear stress strain curve as well as the normal stress strain curve for the compression domain of stresses transverse to fibre direction of GFRP and CFRP shows a distinct non-linearity.
The main reason for this is microdamage within the matrix and at the fibre/matrix interface which develops above a certain stress level but long before the macroscopic IFF.
In a realistic lamina-by-lamina fracture analysis this non-linearity has to be taken into account.
According to VDI-guideline 2014 part 3 the implemented non-linear lamina-by-lamina fracture analysis applies the loads in small load steps.
Instead of using the engineering constants Young’s modulus and shear modulus the secant moduli are used in the non-linear fracture analysis, which are taken from the corresponding stress-strain diagram.
Continuous modulus reduction (degradation) after IFF
If the fracture condition for IFF is satisfied for a lamina, it is necessary to check whether the normal stress acting in the ensuing parallel-to-fibre fracture plane is a transverse tensile or a transverse compressive stress.
If a transverse tensile stress is acting or a low compressive stress in combination with a shear stress, as the load increases there arise more and more cracks running transverse to the lamina plane until under certain circumstances a situation occurs where the lamina is “saturated” with cracks – in other words, the smallest spacing between cracks has been reached.
As a consequence, the mechanical properties have to be reduced to consider the effect of IFF.