Interlaminar stresses at the free corners of a laminate

Becker, Wilfried; Jin, Peipeng; Neuser, P.

doi:10.1016/s0263-8223(99)00019-7

Cited by 29 publications

(29 citation statements)

References 15 publications

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“…3) along the x 1 -axis, there is an obvious deviation of the results of the present FE computations with regard to those of Ref. [8], which meant significantly lower values. This shows the obvious dependence of the peeling stress on the density of the FE mesh even at a distinct distance from the interface between the plies 3 and 4.…”

Section: Considering the Interlaminar Normal Stress Rcontrasting

confidence: 78%

“…The closed-form analysis is compared not only to the present FE results, but also to the results given in [8], as far as available. In contrast to the 2D analysis of the pure free-edge effect, where only one singular point in the interface at the free edge exists, the present fully 3D approach includes the free-edge effect along the corresponding interface lines.…”

Section: Results For a [90˚ 0˚] S -Laminatementioning

confidence: 99%

“…Figures 3 and 4 display the resulting distributions of some interlaminar stresses due to a temperature increment of DT ¼ 100 K. The resultant parameters u, / 1 , / 2 , k 1 , k 2 , g are given in Table 2. A detailed discussion of the qualitative distributions of the stresses for the presently discussed cross-ply layup is omitted here for brevity, this has already been done at some length in [8]. It should only be stated here that the special free-corner effect situation is limited to a corner region with approximate inplane dimensions of about one laminate thickness d.…”

Section: Results For a [90˚ 0˚] S -Laminatementioning

confidence: 99%

“…The following approach is a fully 3D extension of the analysis given in [8], where a somewhat simplified approach of the form (1) was used for pure cross-ply laminate layups. The present analysis is a generalized form of this procedure and offers a more sophisticated yet rewarding approach to the free-corner stress field.…”

Section: Closed-form Analysis For Cross-ply Laminatesmentioning

confidence: 99%

“…We shall denote this as a simplified CP case, whereas the complete analysis is designated as the general CP case. If the remaining two constants u and g are merged into one single parameter u, then the present analysis yields the approach given in [8].…”

Section: Closed-form Analysis For Cross-ply Laminatesmentioning

confidence: 99%

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Three-dimensional closed-form analysis of the stress field at rectangular corners of layered plates

Mittelstedt

Becker

2003

Archive of Applied Mechanics (Ingenieur Archiv)

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A refined and expanded closed-form analytic tool for the calculation of the stress field at free corners of thermally loaded cross-ply and angle-ply laminate structures is developed. Based on adequate approximations for the inplane stresses, the integrated equilibrium conditions yield a full-scale 3D stress field in the vicinity of a free corner. After adjusting the stress field to stress-free conditions at the free edges and facings and obeying conditions of continuity at the interfaces, the remaining free parameters in the stress representation are calculated by minimization of the complementary potential of the laminate. Comparison of the closed-form results with finite element computations shows a good agreement.Keywords Composite, Laminate, Free-edge effect, Free-corner effect, Stress localizations, Closed-form analysis IntroductionClassical laminate plate theory (CLPT) with its assumption of a layerwise plane state of stress in combination with Kirchhoff's kinematical assumptions is a widespread tool for the analysis of composite laminates. However, in real composite laminates, regions with 3D stress concentrations may be found where the stress predictions by CLPT need refinement. A well-known phenomenon of this class is the so-called free-edge effect, i.e. the occurrence of a fully 3D singular stress field in a relatively small boundary region at straight free edges of composite laminates under mechanical and/or thermal load. Depending on the stacking sequence of the laminate, the arising stresses may be either interlaminar normal stresses or interlaminar shear stresses or both, which decay with increasing distance from the free edge. In the inner regions of the laminate, the predictions of CLPT are then fully recovered. Interlaminar stresses in boundary regions may lead to premature failure of the laminate, e.g. by delamination. Basically, different elastic properties of the laminate plies give rise to these singular stress concentrations.Since the pioneering work of Pipes and Pagano, [1], the free-edge effect has been the topic of countless investigations. Numerical methods like FEM or finite difference (FD) analysis have been applied as well as several closed-form analytical approaches attempted, which of course can only provide an approximate insight, for an exact closed-form solution is unknown. Detailed surveys on the free-edge effect have been presented in e.g. [2][3][4][5].A related and advanced stress-concentration problem in the analysis of composite laminates can be found at free corners of layered structures. Here, the stress field is of a full 3D nature. As a first step it may be treated as a superposition of two free-edge effects, which combine to some kind of a ''free-corner effect''. Since numerical analyses of stress concentration problems in composite laminates are often tedious and involve much computational effort, the present work is devoted to an approximate closed-form analysis of the free-corner effect. We consider the case of a thermally loaded layered structure. Here, adequate app...

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Section: Considering the Interlaminar Normal Stress Rcontrasting

confidence: 78%

Section: Results For a [90˚ 0˚] S -Laminatementioning

confidence: 99%

Section: Results For a [90˚ 0˚] S -Laminatementioning

confidence: 99%

Section: Closed-form Analysis For Cross-ply Laminatesmentioning

confidence: 99%

Section: Closed-form Analysis For Cross-ply Laminatesmentioning

confidence: 99%

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