OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 112 The co-ordinate system is the ply co-ordinate system, where i and n refer to the directions 22, 33, 12, 13 and 23. 4.2.3 When the combination between the stress components in several directions shall be taken into consideration, the design criterion for matrix cracking is given by: where, n the co-ordinate system is the ply co-ordinate system, where n refers to the directions 22, 33, 12, 13 and 23 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 = 1.15. Guidance note: A resistance-model factor γ Rd = 1.15 should be used with this design rule. The model factor shall ensure a conservative result with respect to the simplifications made regarding the treatment of combined loads. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- Guidance note: This design criterion is often not available in finite element codes or other commercial software. The Tsai-Wu criterion can be used instead to check for matrix cracking, if the following modifications are made to the strength parameters: - the ply strengths in fibre direction may be chosen to be much (1000 times) higher than the actual values - the interaction parameter f 12 =0 shall be set to 0. It is, however, recommended to use the Puck criterion to predict matrix cracking, see [4.3]). ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 4.2.4 The characteristic strength σ nk for each of the stress components σ nk and the corresponding coefficients of variation COV n are defined as specified in Sec.4 [1.6]. 4.2.5 The combined COV comb of the characteristic strength ∧ σ nk is defined according to one of the following alternatives. The second alternative is conservative with respect to the first. or where: COV comb = max n (COV n ) n the co-ordinate system is the ply co-ordinate system, where n refers to the directions 22, 33, 12, 13 and 23 COV n COV for stress component n COV comb COV for the combined stress components. 4.2.6 When two or more loads are combined, each stress component σ nk in direction n can be the result of several combined loads. In that case each stress component σ nk j , which is the local load effect of the structure in direction n due to load j, shall be considered separately as an individual stress component to determine the COV. or γ . γ F ∧ Sd COV COV . γ M matrix comb comb . γ Rd . ∑ n ⎛ ⎜ ⎜ ∧ ⎝ σ σ nk matrix nk ⎛ ∧ ⎞ ⎛ ∧ = ⎜∑ σ nk . COVn ⎟ / ⎜∑ σ ⎝ n ⎠ ⎝ n ⎛ j ⎞ ⎛ = ⎜∑σ . COVn ⎟ / ⎜ nk ∑ ⎝ n ⎠ ⎝ n COV comb. = max n (COV n ) nk ⎞ ⎟ ⎟ ⎠ 2 ⎞ ⎟ ⎠ j σ < 1 nk ⎞ ⎟ ⎠ DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 113 Guidance note: This approach is conservative compared to the approach of Tukstra’s rule as used for the fibre design criteria. This approach has been chosen for simplification. In the case of fibre failure, only the strains parallel to the fibre directions have to be considered, whereas for matrix cracking all stress directions may interact. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 4.2.7 The choice of the partial safety factors shall be based on the most conservative partial safety factors obtained when treating each stress component σ nk j , which is the local load effect of the structure in direction n due to load j, as a single load. 4.2.8 The partial safety factors γ F and γ M shall be chosen as described in Sec.8 with COVs equal to COV comb , as described in [4.2.5] and [4.2.6]. 4.2.9 Matrix failure cannot be checked on a laminate level, it shall always be checked on a ply level. 4.3 Matrix failure based on Puck's criterion 4.3.1 Matrix cracking can be predicted using the criterion from Puck. It is probably the design criterion that describes the physics of the process the best. 4.3.2 The criterion evaluates the stress state over all possible failure surfaces. The orientation of the failure surface is described by the angle θ. The stress state σ n , τ nt , τ nl in the co-ordinates of the failure surface described by θ is obtained from the ply stresses by: In addition, the stress component σ II in fibre direction is needed. σ II = γ f · γ Sd · γ M · Rd σ 1 Failure is evaluated based on the stress state σ n , τ nt , τ nl for all angles q between - 90 and + 90 degrees. The design criterion is: if σ n (θ) ≤ 0 max ⎡ + 2 2 2 + F ( ( )) ( ( )) ( 1( )) ( ) ⎤ f σ II + Fnnσ n θ + Fntτ nt θ + Fnlτ n θ + Fn σ n θ < 1 ⎢⎣ ⎥⎦ for all θ with –90 ≤ θ ≤ 90, if σ n (θ) < 0 ⎧σ n ⎫ ⎪ ⎪ ⎨τ nt ⎬ = γ F . γ ⎪ ⎪ ⎩τ n ⎭ . γ . γ 2 ⎡ c ⎢ . ⎢ − sc ⎢ ⎣ 0 2 ( c 2 sc − s 2 Sd M Rd 1 0 0 s sc ( c = cosθ; s = sin θ) 2 ) 0 0 s ⎧σ 2 0 ⎤ ⎪ ⎪ σ 3 ⎥ 0 ⎥ ⎨τ 23 c ⎥ ⎪ ⎦ τ 31 ⎪ ⎪⎩ τ 21 ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪⎭ max ⎡ Ff σ II + ⎢⎣ − 2 2 2 − ( F σ ( θ) ) + ( F τ ( θ) ) + ( F τ ( θ) ) + F σ ( θ) ⎤ < 1 nn n nt nt nl n1 n n ⎥⎦ for all θ with –90 ≤ θ ≤ 90, where, σ 1 , σ 2 , σ 3 , σ 12 , σ 13 , σ 23 characteristic values of the local load effect of the structure (stress) in the coordinates of the ply. γ F partial load effect factor (see [4.3.7]) γ Sd, partial load-model factor (from structural analysis see Sec.9) γ M partial resistance factor (see [4.3.7]) γ Rd partial resistance-model factor (see [4.3.8]) F ik strength factors (see [4.3.3]). 4.3.3 The strength factors F ik are functions of the ply strength σ ∧ σ ∧ parameters matrix , matrix , shear , fibre , fibre σ ∧ σ ∧ , and shape parameters of the failure surface. 2t 2c 12 1t σ ∧ 1c The factors are defined as: F f 1 = , if σ ≥ 0 and fibre II A t σ 1t DET NORSKE VERITAS AS
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OS-C501

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