Failure criteria for fiber-reinforced plastics

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Failure criteria for fiber-plastic composites (FRP) serve to distinguish whether an external load in a component made of fiber-plastic composite (see also laminate ) leads to failure or not. The term “failure criterion ” is more common for FRP, since this generic term encompasses the “ breakage criteria ” for the fiber, the matrix, the fiber-matrix interface and the delamination of layers.

Due to the structural anisotropy of fiber-plastic composites, a distinction is made between different types of failure. There are a number of criteria, the application of which depends on the problem to be calculated. The results of the criteria often differ considerably.

In German-speaking countries, the VDI guideline  2014, sheet 3 ( development of components made of fiber-plastic composite - calculations ) is an attempt to introduce a uniform calculation method.

Problem

In the case of metallic materials , the static strength verification is often based on the ratio of a comparison stress (e.g. von Mises stress ) to a strength value obtained from the uniaxial tensile test . A reserve factor can be determined.

This procedure is not possible with fiber-plastic composites because

  • different strengths exist in the different spatial directions (anisotropy),
  • the components “fiber” and “matrix” as well as their interfaces are loaded differently
  • the components have very different properties.

Therefore, a very precise distinction must be made between external stress and internal stress . In addition, some criteria assume that the breaking resistance interacts with the type of stress.

The breaking load of fiber-plastic composites cannot yet be calculated with the same accuracy as with metallic materials due to more complex strength parameters. The strengths in fiber plastic composites react z. Sometimes very sensitive to changes in the following parameters:

Characteristic values, d. H. mechanical properties for the design of fiber-plastic composites, e.g. B. obtained by the tension-compression-torsion test (ZDT test).

Classification

Since fiber-plastic composites typically a laminate, ie layered, have structure, some may damage history observed. Therefore, breakage or failure criteria relate to the beginning ( first ply failure ), the degradation (gradual failure ) or the (catastrophic total) failure of a structure.

What all failure criteria have in common is that the stresses and, in some cases, also the deformation energies are evaluated. Depending on the criterion, physically justified or unjustified adjustments via parameters are included in the mathematical formulation.

The criteria for fiber-reinforced plastic composites are divided according to the type of failure statement:

Flat-rate criteria

General criteria can only differentiate between failure and non-failure, but they do not make any statement about the type of break that occurs (break mode ), i.e. whether the fiber or the matrix will break. Experienced designers can, however, infer the shape of the fracture from the general criteria (with knowledge of the prevailing type and direction of load):

Differentiating criteria

Differentiating criteria only apply to a certain type of break, fiber break or inter- fiber break . With them a prediction of different fracture forms ( fracture modes ) is possible.

The differentiating criteria are closely linked to the classical laminate theory , since the global loads must first be converted in terms of their effect on the individual layer of a laminate. The criteria are then related to the local stress state in the individual layer.

Fiber breakage criteria

Shape possible fiber breakage . The breaks are caused by different loads

A fiber break is the break of a fiber. The fiber is severed by a tear that is perpendicular or inclined to the fiber axis.

Inter-fiber break criteria

Form possible inter- fiber breaks. The breaks are caused by different loads

Inter- fiber break is a break or crack in the matrix ( cohesive failure) or in the interface between fiber and matrix ( adhesive failure); there are no cut fibers.

Delamination criteria
Delamination of CFRP under the influence of compressive force

As delamination refers to the separation of two layers in a layered Fiber-reinforced plastic. Delamination can be viewed as a special case of inter-fiber breakage. The classification is based strongly on the fracture mechanics and divides the loads leading to failure into three categories:

  • Normal load at shift level (Mode I)
  • Shear load in the layer plane, parallel to the fiber orientation (mode II)
  • Shear load in the layer plane, perpendicular to the fiber orientation (mode III).

The loads do not occur in their pure form in the real component . Accordingly, the test technique for characterizing the delamination behavior is based not only on the pure loads but also on their combinations:

  • Mode I tested by DCB ( double cantilever beam )
  • Mode II tested by ENF ( end notch fixture )
  • Mode I + II tested by MMFR ( mixed mode fixed ratio ).

literature

  • A. Puck: Strength analysis of fiber-matrix laminates . Hanser, 1996. ISBN 3-446-18194-6 , free download of the book as pdf
  • M. Knops: Analysis of Failure in Fiber Polymer Laminates - The Theory of Alfred Puck . Springer, 2008. ISBN 978-3-540-75764-1
  • DR Moore, A. Pavan, JG Williams (ed.) Fracture Mechanics Testing Methods for Polymers , Adhesives and Composites. Elsevier, 2001. ESIS Publication 28
  • M. Knops, C. Bögle: Gradual failure in fiber / polymer laminates , Composite Science and Technology. Elsevier, Volume 66, Issue 5, May 2006
  • VDI guideline 2014: Development of components made of fiber-plastic composite - calculations, sheet 3 , edition German / English, September 2006

Web links

  • Microscope images of damaged fiber-plastic composites [1]