FAILURE ANALYSIS OF FRP LAMINATES BY MEANS OF PHYSICALLY BASED PHENOMENOLOGICAL MODELS1
Section snippets
INTRODUCTION
Strength analysis of laminates is still underdeveloped compared to the analysis of stresses and strains. Specifically, there is a lack of fracture criteria and degradation models which are both close to physical reality and simple enough for application in engineering design of laminates with optimum strength. Few of the present models meet both requirements.
Significant characteristics of the fracture criteria and degradation models presented in this paper were already described more than 25
REMARKS ON THE ANALYSIS OF STRAINS AND STRESSES
For the analysis of strains and stresses of single plies the well-known classical laminate theory (CLT) is used. However, for application in fracture analysis of FRP laminates it has to be modified in order to include the non-linear relationships between stress and strain. These non-linear effects can be observed, especially in (τ21,γ21) diagrams, but also in (σ2,ϵ2) diagrams if σ2 is a compressive stress.
Several opportunities to include non-linear effects exist, but not all of them are equally
FAILURE CONDITIONS FOR FIBRE FAILURE (FF)
Up to now, a state of stress is regarded as being the limit for fibre failure in a unidirectional composite when, under combined loading, a stress σ1 parallel to the fibres evolves which is equal to the longitudinal strength (tensile strength XT or compressive strength XC) determined by a uniaxial test. Correspondingly, a failure condition for the strain ϵ1 which is parallel to the fibres of a unidirectional laminate is formulated: ϵ1 must be equal to the longitudinal fracture strain, ϵ1T or ϵ1C
FAILURE CONDITIONS FOR Inter-fibre FAILURE (IFF)
In this research field, the greatest improvements have been achieved recently.5, 6, 7, 8, 9, 10 The knowledge gained by experiments with carbon-fibre/epoxy and glass-fibre/epoxy laminates (which are to be analysed in this paper) teaches that unidirectional layers behave in a very brittle manner at failure, particularly at inter-fibre failure. Without any previous macromechanically apparent plastic deformation, abrupt material separation occurs when the specimen reaches the point of failure.[9]
SURVEY OF FRACTURE CONDITIONS AND RELATIONSHIPS BETWEEN SUBSTANTIAL PARAMETERS
Table 1 summarises all fracture conditions used in this paper in a clearly arranged manner. The fracture resistances RA of the stress action plane are already replaced by the strength values YT, YC and S12 as far as possible.
By an additional term fw, a possible influence of the stress σ1 parallel to the fibres on the inter-fibre failure can be included. This is explained in detail in Section 7.1 which deals with degradation by σ1 stresses.
Regarding the physically-based inter-fibre fracture
RESERVE FACTOR AND EFFORT IN THE PRESENCE OF RESIDUAL STRESSES
When no residual stresses exist, the following definition is valid:
The reserve factor fR is the one (positive) factor all existing stresses would have to be multiplied with to originate failure. This means that the stress vector would have to be stretched in its original direction by this factor in order to cause fracture.
In Fig. 7, such an increase of stresses can be seen in the stretching of the stress vector {σ}(1).
If residual stresses (index r) {σ}(r) exist, it is only possible to define a
Degradation of fracture resistances in the inter-fibre fracture conditions due to single fibre failure
Since fibre strength follows a statistical distribution, single fibres already break under uniaxial σ1 tensile stress long before fracture of many fibres leads to ultimate failure when XT is reached. These preliminary single fibre breaks cause local damage in the vicinity of the breaks in the form of debonding of fibre and matrix and microcracks in the matrix. By this damage the fracture resistances RA the composite offers to inter-fibre fracture are decreased. This is taken into account by
General procedure
According to the given problem, only the procedure for a load increasing monotonically from zero load to fracture is discussed here. The described calculation models and procedures are utilised by our computer program NOLI FRAN COLAM (non-linear fracture analysis of composite laminates). The laminates analysed are described elsewhere.[25]
When manufacturing laminates, residual stresses develop both as a result of shrinkage when curing the matrix, and most of all as a consequence of cooling the
THEORETICAL RESULTS
The theory described above was applied to predict the behaviour of laminates supplied by the organizers.[25] In the analysis, the lamina properties of the four materials (T300/914C, AS4/3501-6, E-glass/MY750 epoxy and E-glass/LY556 epoxy) investigated were taken from the data provided.
Fig. 10 shows the failure envelope for the E-glass/LY556 unidirectional lamina subjected to combined transverse and shear loading (σy,τxy). Three modes of failure are predicted depending upon the state of stresses
CONCLUDING REMARKS
The introduction of new inter-fibre fracture criteria, which are based on the brittle failure behaviour of composites, makes fracture analysis even more realistic than it has been with the methods described previously.[1] In addition, the new criteria make a distinction between different fracture modes (A, B and C) possible.
Furthermore, application of separate fracture criteria for fibre failure and inter-fibre fracture provides a rapid overview of the fractures which can be expected for a
Acknowledgements
The authors would like to thank Mrs Professor Dr R. Jeltsch-Fricker, Kassel, for discussion of mathematical aspects and Dr-Ing. D. Huybrechts, Aachen, for discussion of engineering aspects. The skillful typing of Mrs M. Streb is gratefully acknowledged. Thanks are due to Dipl.-Ing. S. Wenzel for computation and to Dipl.-Ing. A. Knickrehm for translation of the manuscript.
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