S5-1 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation SECTION 5 FAILURE CRITERIA FOR COMPOSITES

S5-2 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation

S5-3 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation CALCULATING MATERIAL STRENGTH n For isotropic materials the resulting stress (or strains) are compared with a single value characterizing the allowable strength of the material. Generally, the maximum shear stress (Tresca) or shear energy (Von Mises) is used to predict yield of a metal n For orthotropic materials, strengths in different directions can vary widely. For example, a unidirectional lamina could withstand a tension of 2000 MPa along the fibres, but fail under a tension of 100 MPa perpendicular to the fibres. This brings the need for special purpose algorithms for calculating the allowable strength for composites n Failure criteria discussed here are limited to first-ply failure, giving a conservative estimate of the strength of the laminate n Commonly used failure criteria are generally empirical, and do not reflect micro-mechanical failure mechanisms

S5-4 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation FAILURE MECHANISMS OF UNIDIRECTIONAL LAMINA Longitudinal Tension - Fiber Failure Longitudinal Compression - Fiber Failure Transverse Tension - Matrix Failure Transverse Compression - Matrix Failure In-Plane Shear - Fiber/Matrix Interface Failure

S5-5 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation STRENGTH COEFFICIENTS For Orthotropic lamina under plane stress, up to eight strength coefficients are commonly used to describe strengths: Xt TXTensile strength along the x-axis Xc CXCompressive strength along the x-axis Yt TYTensile strength along the y-axis Yc CYCompressive strength along the y-axis S12 SXYShear strength in the XY plane S23 SYZShear strength in the YZ plane S31 SXZShear strength in the XZ plane F12Interaction Term The numbers should be input as absolute values

S5-6 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation n Failure is determined using a mathematical function of load vs. strength. Several mathematical models are used to predict failure. n Failure Index (FI) is calculated based on the load and strength according to several models (see later slides) n Strength Ratio (SR) is the ratio by which the load must be factored to achieve failure. It is usually derived from the Failure Index u A margin of safety (MoS) is a reflection of the reserve strength DEFINITIONS x y a b Failure Surface in Stress Space

S5-7 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation MAXIMUM STRESS FAILURE CRITERION n Direct comparison of stresses and strength coefficients n Ignores interaction between loads in different directions

S5-8 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation HILL FAILURE CRITERION Where: F 11 = 1 / TX 2 for σ x 0 F 12 = -1 / (2TX 2 ) for σ x σ y 0 1 / CX 2 for σ x < 0 -1 / (2TY 2 ) for σ x σ y < 0 F 22 = 1 / TY 2 for σ x 0 F 66 = 1 / SXY 2 1 / CY 2 for σ x < 0 n Does not automatically account for difference in tensile and compressive strengths

S5-9 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation HILL FAILURE CRITERION (Cont.) n In MSC.Laminate Modeler the Hill criteria is supplemented by a maximum criterion for through- thickness shear loading causing matrix failure SR m = 1 / FI m MoS m = SR m -1 n The lower of the in-plane and through plane margins of safety is output.

S5-10 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation TSAI-WU FAILURE CRITERION Where: F 1 = 1/TX-1/CXF 22 = 1/(TY CY) F 2 = 1/TY-1/CYF 12 = IXY/sqrt(TX CX TY CY) F 11 = 1/(TX CX)F 66 = 1/SXY 2 IXY recommended = -0.5 (only important for multiaxial loading) Where: n Accounts for different tensile and compressive strengths by incorporating linear terms

S5-11 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation TSAI-WU FAILURE CRITERION (Cont.) n In MSC.Laminate Modeler the Tsai-Wu criteria is supplemented by a maximum criterion for through- thickness shear loading causing matrix failure SR m = 1 / FI m MoS m = SR m - 1 n The lower of the in-plane and through-thickness margins of safety is output

S5-12 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation COMPARISON OF MAXIMUM AND TSAI-WU y x TX - CX TY -CY Tsai-Wu Maximum

S5-13 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation OTHER QUADRATIC FAILURE CRITERIA n These are similar to Tsai-Wu criterion, except with different interaction terms n HOFFMAN F 12 = -0.5 / (TX CX) n HANKINSON F 12 = 0.5 / (1 / (TX + CY) + 1 / (TY+CX) – 1/ SXY 2 ) n COWIN F 12 = 1 / sqrt (TX CX TY CY) –0.5 / SXY 2

S5-14 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation USER DEFINED FAILURE CRITERIA n MSC.Laminate Modeler allows the user to define a custom failure criterion n The user writes a custom function (using a PCL function) and selects user failure criterion for calculation n The model could for example include microstructural failure models or multiple sub-criteria models, each with a particular mechanism of failure

S5-15 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation HOW CREATE USER DEFINED FAILURE CRITERION n Define a function user in class p3CM_create_res_fail_user u Inputs are automatically read as result tensors and material allowable arrays. u Output is an array of margin, critical component, and failure index. n Example on next slides uses V2003 functions n Having defined the PCL function, compile it into MSC.Patran u !!input user_def_crit.pcl n If there are no compiler errors given in the history window start using user defined criterion

S5-16 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation EXAMPLE: USER DEFINED FAILURE INDEX (V2003) CLASS p3CM_create_res_fail_user function name(theory) string theory[] theory = "BigBang" end function /* name */ function relevant_cols(num_valid_cols, valid_labels) integer i integer num_valid_cols logical valid_cols() string valid_labels[]() num_valid_cols = 1 valid_cols(1) = TRUE valid_labels(1) = "dummy" for (i = 2 to 8) valid_cols(i) = FALSE valid_labels(i) = "" end for return (TRUE) end function /* relevant_cols */ function check_mat_allow_valid(num_mats, mat_ids, mat_names, mat_allows) integer num_mats integer mat_ids() real mat_allows() string mat_names[]() dump num_mats, mat_ids, mat_names, mat_allows return (0) end function /* check_mat_allow_valid */ function user(res_array, mat_array, out_res_array) real res_array(), mat_array(), out_res_array() real sxx, syy, sxy real margin1, margin2, marginf real first1, second, epsa, gama real first2

S5-17 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation /* * Set input values. */ sxx = res_array(1) syy = res_array(2) sxy = res_array(4) /* * Initialize variables. */ margin1 = 0.0 margin2 = 0.0 marginf = 0.0 epsa = 4.39e-3 gama = 1.5e-2 out_res_array(1) = 0.0 out_res_array(2) = 1.0 out_res_array(3) = 1.0 /* * Calculate margin of safety 1 */ first1 = ((sxx/epsa)**2) second = ((sxy/gama)**2) margin1 = (1/((first1 + second)**.5) - 1.0) /* * Calculate margin of safety 2 */ first2 = ((syy/epsa)**2) second = ((sxy/gama)**2) margin2 = (1/((first2 + second)**.5) - 1.0) /* * Compare the two margins */ if (margin1 < margin2) then marginf = margin1 else marginf = margin2 end if /* * Set output values. */ out_res_array(1) = marginf out_res_array(2) = margin1 out_res_array(3) = margin2 /* * John Klintworth THIS FUNCTION MUST RETURN 0 IF SUCESSFUL */ return 0 end function /* user */ end class EXAMPLE: USER DEFINED FAILURE INDEX (V2003) (Cont.)

S5-18 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation STRAIN-BASED CRITERIA n All failure criteria can be based on strain rather than stress n Failure strain varies less than failure stress. Thus, can make criteria more stable. n Allowables and results must use same measure of strain (e.g. shear strain allowables must be tensor shear strains, not engineering shear strains)

S5-19 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation MSC.PATRAN INPUT OF ALLOWABLES n Materials u 2D Orthotropic u Input Properties… l Constitutive Model: n Failure l Failure Limits: n Stress

S5-20 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation MSC.LAMINATE MODELER USER INTERFACE n In MSC.Laminate Modeler, method of failure calculation is specified in the Result menu Select output entities Input material allowables (see next slide) Select failure criterion Select application region (surfaces or elements) Select the proper load and subcases

S5-21 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation NOTE: If the constants are already entered in MSC.Patran, they will automatically show up in the laminate modeler as well MSC.LAMINATE MODELER USER INTERFACE

S5-22 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation CALCULATING FAILURE STATE ORDER OF DETERMINING n Using MSC.Laminate Modeler the failure calculations are done by post processing, based on the solver(MSC.Nastran) results. This is a different approach compared to having the solver do the failure calculation; the solver does the simulation as an add-on to the deflection and stress calculation. n This approach allows a more easily and quicker performed what-if study. In order to do a new failure calculation, for example with a different criteria, it is not neccesary to re-run the solver. n The failure calculation can be done on user-specified local areas of the model. There is no need to include the entire model.

S5-23 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation n Perform Workshop 2 Failure Criteria for Flat Plate, and Workshop 3 Flat Plate Using MSC.Laminate Modeler in your exercise workbook n Be sure to ask for help on anything you dont understand EXERCISES

S5-24 PAT325, Section 5, February 2004 Copyright 2004 MSC.Software Corporation