OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 110 σ x ∞ x σ x 2R y σ x ∞ Figure 6-4 Infinite plate with a circular hole For an infinite orthotropic plate, with a crack, subjected to a uniform stress, σ x ∞ , applied parallel to the x-axis at infinity, the normal stress, σ x , along the y-axis ahead of the crack tip, see the Figure 6-5, can be expressed as: σ σ x ( 0, y) = for y c x > 2 2 y ∞ σ x ∞ y − c x σ x 2c y Figure 6-5 Infinite plate with sharp crack σ x ∞ The equations above are valid for infinite plates. For finite plates, it is necessary to add a Finite Width Correction (FWC) factor. There are several analysis methods, including finite element methods, to determine the FWC factor. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 3.6.8 If certain damage is expected to be present in the structure at various points that can cause stress concentrations, the structure shall be analysed by modelling the presence of this damage. The damage shall be placed into the structure in a representative and conservative way. 3.6.9 As an alternative to analysing the structure with various points of damage the structure can be analysed with a reduced strength that represents the damage. All strength values used in the design criteria shall be based on measurements from damaged laminates (see Sec.4 [1.7]). DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 111 4 Matrix cracking 4.1 General 4.1.1 Matrix design criteria apply to a matrix in a ply where the deformation of the matrix is restrained by the fibres of the ply or the surrounding laminate. Guidance note: Matrix cracking is a simple concept at first sight but quite involved in details. Some laminates have already matrix cracks after manufacturing. These cracks can be introduced by thermal stresses or by shrinkage of the matrix during cure. Laminates without matrix cracks have an initial ply stress when the first cracks start to form. Once cracks are formed they start to propagate at higher ply stresses and additional cracks are formed. Crack formation will eventually lead to a change in stiffness. This point is usually referred to as the matrix crack point or first ply failure etc., because this is what can easily be measured. Eventually laminates show crack saturation and no further cracks form when loaded more. The change of modulus has been related to matrix crack density in some publications. See [1.1.2] and [1.1.3] for relevance of matrix cracking for a particular application. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 4.1.2 Matrix cracking is defined here as the onset of matrix cracking. The increase of the number of matrix cracks at higher stresses or strains is not covered by the matrix cracking criteria presented in this section. 4.1.3 Characteristic strength shall be defined according to Sec.4 [1.6]. 4.1.4 Matrix cracking shall be checked on the ply level. 4.1.5 Two alternative design criteria may be used. The simple stress criterion ([4.2]) or the Puck criterion ([4.3]). 4.1.6 If the component may fail due to wedge shaped matrix cracks in compression, the Puck criterion must be used to obtain the direction of the failure surface([4.3] and [4.4]). 4.2 Matrix failure based on simple stress criterion 4.2.1 The following design criterion should be used when the stress in one direction is dominating compared to the stresses in the other directions. The stress in one direction is said to be dominating when the criterion in [4.2.2] is not satisfied. where, γ . γ F Sd . σ nk ∧ matrix nk σ < γ . γ n direction of the dominating stress σ∧ nk characteristic value of the local load effect of the structure (stress) in the direction n matrix σ nk characteristic value of the stress components to matrix cracking in direction n γ F partial load effect factor γ Sd partial load-model factor γ M partial resistance factor γ Rd partial resistance-model factor, γ Rd = 1.0 The co-ordinate system is the ply co-ordinate system. Guidance note: The stress to matrix cracking is in general direction-dependent. This is due to the presence of fibres that concentrate the stresses, such that the matrix stress to failure in the direction parallel to the fibres is in generally larger than in the perpendicular direction. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 4.2.2 The combination between the stress components in several directions shall be taken into consideration when the criterion below is satisfied. In that case, there is no dominating stress and the combination cannot be disregarded. max i ∧ σ ik σ ik matrix M σ Rd / ∑ nk ≤ 10 n ≠ i ∧ matrix σ nk DET NORSKE VERITAS AS
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