OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.9 Structural analysis – Page 146 2.6 Two-step non-linear failure analysis method 2.6.1 The method may be applied for both 2-D and 3-D problems, see [1.3.4]. 2.6.2 In the results presented for this method it is assumed that matrix failure occurs prior to fibre breakage, see [2.4.3]. 2.6.3 In the first step response calculations are performed with non-degraded material properties. 2.6.4 In regions (e.g. finite elements) where the strains (or stresses) exceed the level for matrix cracking (or other failure mechanisms), the in-plane material properties are degraded according to the method presented in [2.5.5]. 2.6.5 The final step consists of response calculations with the locally degraded material properties. 2.6.6 If the final calculations break down, e.g. due to ill-conditioned structural matrices, one should repeat the final step with non-degraded through thickness parameters. 2.6.7 For problems related to the local degradation of material properties, see [2.2.7]. 2.6.8 For difficulties arising in numerical calculations when using locally degraded values equal to 0, and the possibilities to apply larger values for the degraded parameters, refer to [2.2.4] and [2.2.5]. 2.6.9 Before matrix cracking (and other kinds of failure mechanisms) the method predicts correct response values provided that the underlying analytical or numerical (FE) analysis method is applied within its assumptions and limitations (see under [4] and [5]). 2.6.10 After local occurrences of matrix cracking statically determined problems result in: — laminate stiffness – generally correct, locally too low — laminate stresses – correct — laminate strains – generally correct, locally too large — ply stiffness – generally correct, locally E 1 is correct and the other ply properties are mostly too small — ply stresses – generally correct, locally σ 1 is too large and the other stress components are mostly too small (zero) — ply strains – generally correct, locally too large. 2.6.11 After local occurrences of matrix cracking problems with known displacements result in: — laminate stiffness – generally correct, locally too low — laminate stresses – generally correct, locally too small — laminate strains – correct — ply stiffness – generally correct, locally E 1 is correct and the other ply properties are mostly too small — ply stresses – generally correct, locally σ 1 is correct and the other stress components are mostly too small (zero) — ply strains – correct. 2.6.12 After local occurrences of matrix cracking statically indeterminate problems result in: — laminate stiffness – generally correct, locally too low — laminate stresses – generally correct, locally between too small and correct — laminate strains – generally correct, locally too large — ply stiffness – generally correct, locally E 1 is correct and the other ply properties are mostly too small — ply stresses – generally correct, locally σ 1 is too large and the other stress components are mostly too small (zero) — ply strains - generally correct, locally too large. 2.6.13 The applicability of this method in conjunction with various failure mechanisms is discussed under [3]. 2.7 Through thickness 2-D analysis 2.7.1 [2.2] deals with an in-plane 2-D analysis method that is applicable if through thickness stresses can be neglected, see [1.3.4]. The in-plane 2-D approach is frequently used in conjunction with global analysis of relatively large composite structures. 2.7.2 On the other hand, certain structural details, in which plane strain conditions prevail, may be analysed by a through thickness (cross section) 2-D approach. DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.9 Structural analysis – Page 147 Guidance note: Examples on problems that may be analysed by the through thickness 2-D approach include several adhesive bonded joints with a width to thickness ratio that is much larger than unity and certain effects related to bolted joints, including pre-tension, in which symmetric conditions along axes prevail. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 2.7.3 All the analysis methods that are applicable for in-plane 2-D problems (presented in [2.2], [2.4], [2.5] and [2.6]) may be adopted to through thickness 2-D analysis. 2.7.4 The simplifications introduced in the through thickness analysis shall be carefully investigated to ensure that no crucial effect is lost. 3 Connection between analysis methods and failure criteria 3.1 General 3.1.1 In this section the connection between the analysis methods from [2] and the failure criteria from Sec.6 is presented, see Table 9-2. 3.1.2 Progressive failure analysis is applicable for all kinds of failure criteria. 3.1.3 However, as can be seen from Table 9-2, the simplified analysis methods are also applicable in conjunction with several failure criteria. Table 9-2 Analysis methods and their failure criteria Analysis Method Failure Progressive Linear non-degraded Linear degraded Two-step non-linear criteria Fibre failure Yes Yes (see [3.2.1]) Yes Yes Matrix cracking and Yes First occurrence No (it is assumed that First occurrence delamination matrix cracking has already occurred) Yielding Yes Onset of yielding No (see above) Onset of yielding Maximum deformation Yes No Yes Yes 3.2 Modification of failure criteria 3.2.1 In order to obtain conservative predictions of fibre failure from the linear non-degraded method (see [2.4.7] and [2.4.9]) a partial analysis factor, γ A , shall be introduced for the fibre failure criterion related to each fibre direction of the laminate. 3.2.2 For each fibre direction of the laminate the partial analysis factor shall be given by γ A = E lin /E nonlin , where E lin and E nonlin are laminate moduli (stiffness) related to loading in the fibre direction of consideration. E lin is the laminate stiffness based on initial (non-degraded) ply properties, while E nonlin is the reduced laminate stiffness obtained from degraded ply properties (see [2.5.5]). A further explanation is provided by Figure 1 and the guidance note below. Guidance note: The introduction of partial analysis factors, γ A, above may be thought of as a reduction of the effective strain to failure from εˆ toεˆ corr (mean values). Figure 9-1 shows a typical laminate stress-strain curve for a laminate containing 0, 45 and 90 layers when loaded in the 0 direction. A partial analysis factor shall be calculated for each fibre direction of the laminate, which in this example corresponds to obtaining laminate stress-strain relations for loading in the 0, 45 and 90 degrees directions for the laminate in Figure 9-1. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- DET NORSKE VERITAS AS
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