Module for 3D representation of failure criteria in the stress space

General

In this module, the failure bodies can be displayed for various failure criteria and strengths. Several failure bodies can be displayed simultaneously [1].

The strength criteria currently implemented are:

• Puck criterion [2] (based on [3] with simplification regarding fiber breakage and a weakening factor for interaction of stresses in the fiber direction and outside the fiber direction)
• ZTL criterion [4], [5],
• Hashin criterion [6],
• FMC (Cuntze criterion) [7], formerly [8],
• Tsai-Wu lumped criterion [9],
• maximum tension criterion,
• Sun criterion [10],
• Rotem criterion [11],
• Edge criterion [12],
• Mayes criterion [13].

Note on the FMC. criterion: From source [7], equation 10b is used instead of the preferred equation 11a in the source. Both equations are only identical for a reserve factor of 1, i.e. for the actual fracture condition. When using equation 11a, it is no longer possible to factor out the reserve factor when multiplying all voltage components by a reserve factor. This means that when using equation 11a, it is no longer possible to multiply all loads by a factor of 10 in the case of a reserve factor of 0.1 and thus achieve a reserve factor of 1. The behavior of the failure criterion becomes non-linear through the use of equation 11a. It is assumed that eLamX² users do not expect such behavior, which could lead to significant errors. In addition, a check is introduced that the numerator must always remain positive in order to avoid mathematically impermissible operations during the exponentiation with m.

Structure

1 - Selection of criteria

There are various failure criteria for the strength of fiber composite layers under multiaxial loading. These are mostly based on empirical or semi-empirical models, which are based on the evaluation of uniaxial tensile and compression tests. The composite layer is regarded as a homogeneous layer. In this window, the criteria to be displayed are selected in the form of the resulting failure bodies.

2 - Parameters

The strength of the composite layer and additional parameters required for the calculation can also be defined. By default, meaningful values are entered for the additional parameters. However, these can be replaced by your own values at any time.

In addition to the actual strengths, there are additional parameters for some failure criteria. These can be entered under “Additional properties”.

3 - Graphical output of the failure bodies

This window shows a three-dimensional representation of the resulting failure bodies for the various criteria. These can be moved, rotated and zoomed to any position by holding down the mouse buttons.

- Rotate

- Zoom

- Move

4 - View options

These buttons can be used to edit the view of the failure bodies. The top three buttons can be used to display the three planes of the three-dimensional stress space. In addition, an isometric representation and an adaptation of the failure bodies to the existing window size are possible. As an additional option, the failure bodies can be displayed with or without meshing.

- View of the x-y plane

- View of the x-z plane

- View of the y-z plane

- Isometric representation

- Adaptation to window size

- Switching the display of the net on and off

[1] I. Kappes. Implementierung von Festigkeitsmodellen für Faser-Kunststoff-Verbunde in eLamX. ILR –LFT G 08-40, Technische Universität Dresden, April 2009.

[2] H. Schürmann. Konstruieren mit Faser-Kunststoff-Verbunden. Springer, 2004.

[3] A. Puck and H. Schürmann. Failure analysis of frp laminates by means of physically based phenomenological models. Composite Science and Technology, 58(7):1045-1067, 1998.

[4] S. Roth and J. Windhövel. Zukunftstechnik- Luftfahrt ZTL, Fasertechnik, Teil B: Mechanische Eigenschaften von Faserverbunden. Technical report, Dornier GmbH Friedrichshafen, 1975.

[5] Kröber. Bruchhypothese und Reservefaktoren für unidirektionale Einzelschichten in Faserverbunden, 1982. HSB 51301-01, Ausgabe A, Jahr 82.

[6] Z. Hashin. Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics, 47:329-334, 1980.

[7] R.G. Cuntze. Efficient 3d and 2d failure conditions for ud laminae and their application within the verification of the laminate design. Composites Science and Technology, 66:1081-1096, 2006.

[8] R.G. Cuntze and A. Freund. The predictive capability of failure mode concept-based strength criteria for multidirectional laminates. Composites Science and Technology, 64:343-377, 2004.

[9] S.W. Tsai and E.M. Wu. A general theory of strength for anisotropic materials. Journal of Composite Materials, Vol. 5:58-80, 1970.

[10] C.T. Sun and J. Tao. Prediction of failure envelopes and stress /strain behaviour of composite laminates. Composites Science and Technology, 58(7):1125-1136, 1998.

[11] A. Rotem. Prediction of laminate failure with the rotem failure criterion. Composites Science and Technology, 58(7):1083-1094, 1998.

[12] E.C. Edge. Stress-based grant-sanders method for predicting failure of composite laminates. Composites Science and Technology, 58(7):1033-1041, 1998.

[13] J.S. Mayes and A.C. Hansen. Composite laminate failure analysis using multicontinuum theory. Composites Science and Technology, 64(3-4):379-394, 2004.