ACDC User Manual Ver. 1.0 Centre Composite December 2016
ACDC, Ver. 1.0 User Manual Centre Composite, 2016 (software@composite.lv) Table of Contents Introduction... 1 System requirements... 1 Theoretical background... 1 Literature... 4 User interface... 4 Materials... 4 Laminate... 5 Plot... 7 Open Hole Strength... 9 Filled Hole Strength... 9 ABD... 10 Appendix: Example... 11 Introduction The ACDC ( Analytical Calculation of Defects in Composites ) program uses the analytical solution of an anisotropic plate with hole to estimate the residual strength of the laminate loaded by membrane forces and bearing load. System requirements Microsoft.Net Framework ver. 4 or higher is required to run this software. Theoretical background The solution of the laminate with hole loaded by the bearing force and far-fields membrane forces is obtained using Lekhnitskii s formalism [1] by decomposing the load into two problems (Figure 1): 1. anisotropic plate with open hole loaded by far-field membrane forces; 2. anisotropic plate with open hole with distributed forces at the boundary of the hole. 1
The second problem is solved using method described in [2]. Superposition of these two solutions gives us the stress/strain state in every point of the laminate. Figure 1 Load decomposition for a pin-loaded hole. The analysis of the residual strength is based on the critical distance theory [3]. The critical distance theory is an empirical method, where it is assumed that failure occurs when the stresses exceed the critical value at some distance from the stress concentration (edge of the hole in our case). This distance is called characteristic distance and is though as a material parameter, allowing to estimate the residual strength of the laminates with stress concentration of different geometries. For the bearing load the ACDC program uses the extension of the method, proposed in [4]. Two characteristic distances should be calculated, one for bearing load, R oc, and second for tensile bypass load, R ot. The bearing characteristic distance is calculated using the critical bearing strength of the laminate, F br. Second characteristic distance is calculated using filled hole tensile strength of the laminate, F FHT (for conservative analysis minimum of the open hole, F OHT, and filled hole, F FHT, tensile strengths is often used). Therefore two strength values should be provided for every laminate to estimate its residual strength. The characteristic distance is defined as a maximum distance along the line of the maximal stress (as shown in Figure 2), where the failure criterion is fulfilled in at least one ply. The failure criterion is one of the: 1. Maximum stress; 2. Tsai-Wu; 3. Yamada-San; 4. Tsai-Hill. After the characteristic distances are determined, the residual strength of the laminate under general loading can be estimated. For this the stress state in each layer is examined along the characteristic line using the same failure criterion and the minimal safety factor determines the residual strength. The shape of the characteristic line is governed by the equation: where R is the hole radius. r(φ) = R + R ot + (R oc R ot )cos (φ) 2
Figure 2 Characteristic curve for a filled hole. For an open hole analysis the modification of the above method is used. Two characteristic curves will be used in this case, one for tensile load and one for compressive load. The curves are represented by ellipses, therefore four characteristic distances need to be calculated, as shown in Figure 3: R 0 c characteristic distance due to compression in X direction; R 90 c characteristic distance due to compression in Y direction; R 0 t characteristic distance due to tension in X direction; R 90 t characteristic distance due to tension in Y direction. To determine four characteristic distances, four laminate strength values are needed: open hole tensile and compressive strengths for the specimens cut in two directions, 0 and 90 degrees respectively. Figure 3 Characteristic curves for an open hole. 3
After characteristic distances are calculated, they can be used to estimate the residual strength of the laminate under combined load. The program will check the stress state in every layer along the two characteristic curves (choosing tensile or compressive curve depending on the stress state in this layer). Fiber failure criterion is used in this problem and the minimum safety factor along characteristic curves in tension and compression will be calculated. Literature 1. S.G. Lekhnitskii, Anisotropic plates. Gordon and Breach Science publishers, 1984. 2. Waszczak J.P. and Cruse T.A., A synthesis procedure for mechanically fastened joints in advanced composite materials. AFML-TR-73-145, Vol. 2, 1973. 3. J. M. Whitney and R. J. Nuismer, "Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations," J. of Composite Materials, Volume 8, July 1974. 4. Garbo S.P. and Ogonowski J.M., Effect of variances and manufacturing tolerances on the design strength and life of mechanically fastened composite joints. Methodology development and data evaluation. AFWAL-TR-81-3041, Vol. 1, 1981. User interface Graphical user interface is used to specify material properties, apply loads and view the results. The main window has six tabs: Materials specify elastic and strength properties of each material; Laminate specify laminate lay-up; Plot visualize the stress field around open or filled hole; Open Hole Strength calculate open hole residual strength; Filled hole Strength calculate filled hole residual strength; ABD laminate ABD matrix and effective properties. Materials Figure 4 Table with material s elastic and strength data. 4
In the Materials tab the materials properties are defined. Each material has a name and sequential number (in the first column). User has to input elastic properties of each material. Strength properties also required for residual strength calculations. Laminate Figure 5 User interface for the definition of the laminate layup. In the Laminate tab the material, thickness and orientation angle for each ply have to be defined. The user may choose the material name from the drop-down menu or input its sequential number in the Mat. Nr. column. For strength calculation and results graphical visualization the laminate should consist of single material and orientation angles should be 0, 45, -45 and 90 degrees. To simplify laminate definition, several additional options are present in this tab. Symmetry dropdown menu allows to create symmetric or anti-symmetric laminates. The current laminate will be mirrored and added to the existing plies to form symmetric or anti-symmetric laminate. If Symmetric / Mid-Ply or Anti-symmetric / Mid-ply options are used, current last ply will be used as mid-ply of new laminate. The Layer thickness option can be used to change the thickness of all layers. Rotate option will rotate all layers by specified angle. Additionally, composite layup stacking sequence may be entered as text string in compressed format, as shown in Figure 6. The notation for layup stacking sequence definition follows ASTM standard D6507-11 (except material codes). Two options are available: 5
1. By pressing Get button, current laminate stacking sequence is analyzed and written in text-box as string in compressed form. 2. By pressing Apply button, the text string from text-box is expanded and resulting stacking sequence will be set as current. The material number and thickness of the first layer will be used for all layers in this case. Figure 6 Laminate layup definition via layers stacking sequence notation. Ply directions and number of layers are indicated using the laminate orientation code as follows: [ 1 m 1 / 2 m 2 / ] ns (or [ 1 :m 1 / 2 :m 2 / ]:ns in computer format), where Examples: 1 ply orientations (degrees) of the laminate staking sequence m 1 number of plies at each particular orientation (not used for single ply) n number of repetitions of the bracketed group of plies s indication of geometric symmetry \ indication of the last ply for mid-plane symmetry +- 1 short format for / 1 /- 1 / sequence ( ) group of plies (nested groups are allowed). Stacking sequence Compressed form 0/90/90/0 [0/90]:s 0/0/90/0/0 [0:2/90\]:s 45/-45/-45/45 [+-45]:s 45/0/90/90/0/0/90/90/0/-45 [45/((0/90):s):2/-45] 6
Plot The stress/strain field around the hole can be viewed in Plot tab (Figure 7). The user has a number of options to specify which stress/strain components will be displayed. The options are divided into several groups: Load the far-fields load can be specified as stress, strain or force per unit length (membrane forces). In addition, for filled hole the bearing force magnitude and direction has to be defined. R is the radius of the hole. Chart / Table options these parameters are only used with Chart or Table options, and allow to specify the direction and the end points of a line, along which the stress/strain components will be calculated. For circumferential direction the radius of an arc and starting and ending angles (in degrees counterclockwise) should be defined. For radial direction the angle of a line and distance from hole center to starting and ending points should be defined. Stress / strain components define which components should be displayed. User can choose between average laminate stresses (in global coordinate system) or stresses and strains in each layer (in layer coordinate system). Stresses or strains can be displayed in Cartesian or polar coordinate system. Checkboxes below allow choosing which components will be displayed (in polar coordinate system X component will be the radial direction). Figure 7 User interface for the definition of the loads and boundary conditions The stress/strain results can be presented in three forms: 7
Isolines shows the stress/strain field in the area around the hole (Figure 7). Chart shows graphs with stress/strain distribution along a specified line (Figure 8). Table the stress/strain data along the line will be written in table, which may be copied to other software for further processing (Figure 9). Several stress/strain components can be chosen for Chart or Table options. For Isolines option only the first selected component will be displayed. Figure 8 Chart plot. Figure 9 Stress components presented in table form. 8
Open Hole Strength Calculates residual strength of the laminate with open hole under general in-plane loading using characteristic distance method. As was discussed in Theoretical background section, this method requires uniaxial strength of laminate (OHT and OHC) in two directions, measured for one specific size of a hole. These data should be entered into Laminate Uniaxial Strength sections (see Figure 10). Radius of hole used in tests should be entered together with strength data. Characteristic distance method allows to estimate residual strength of laminate with holes of different sizes, therefore the hole radius for with calculation will be performed should be entered in the Output section. Press the Calculate button and the program will calculate four characteristic distances and two safety factors (for tension and compression respectively). Figure 10 Open hole residual strength calculation. Filled Hole Strength Calculates residual strength of the laminate with filled hole under general in-plane load and bearing force. As was discussed in Theoretical background section, this method requires FHT and Bearing strength of laminate, obtained for the size of a hole of interest. These data should be entered into Laminate Strength sections (see Figure 11). Radius of the hole should be entered together with strength data as well as choice of failure criterion. The far-fields load specified as force per unit length (membrane forces) and its angle () with respect to zero ply with the bearing force magnitude (P) and direction () should be entered into 9
Load sections. Press the Calculate button and the program will calculate two characteristic distances and safety factor. Figure 11 Filled hole residual strength calculation. ABD The ABD tab displays the ABD matrix, ABD inverse matrix and effective properties of the laminate (Figure 12). Figure 12 ABD matrix and effective properties of the laminate 10
Appendix: Example Let us define test problem to compare results with MSC.Patran solution: analysis of stress-strain state of filled hole (D = 6.35 mm) laminate under the following loads N x = 12 N/mm, N y = -4 N/mm, P = 150 N, β = 0 (bearing force is directed along x axis). The thickness of the layers is 0.2 mm and the laminate lay-up is [0/90] s. Elastic properties of the monolayer are given in Table 1. Running the analysis Table 1 Elastic properties of the material E 11, MPa E 22, MPa G 12, MPa 12 143000 9300 5520 0.29 Start the program and enter the material and the laminate data using Materials and Laminate tabs like shown in Figure 13 and Figure 14. Then go the Plot tab to enter loads and hole radius and then, after choosing the desired results in section Stress / Strain components like Average/Layer, Stress/Strain, Cartesian/Polar, corresponding layer and stress or strain component, press Isolines/Chart/Table button on the same tab (Figure 15). Solution should be completed in several seconds. Figure 13 Input data: elastic properties of material Figure 14 Input data: laminate lay-up 11
Stress, MPa Figure 15 Results: stresses σ x in 0 plies Results After the solution is complete, the results will be shown on the left in the Plot tab. In Figure 15 there is an example of σ x stresses in 0 plies in case of Isolines. Figure 16 shows comparison of results obtained in AC/DC and MSC.Patran: σ x stresses in 0 plies taken from hole edge. 250 200 150 100 50 Patran AC/DC 0-50 -100 0 60 120 180 240 300 360 Angle, ⁰ Figure 16 Results: comparison of σ x stresses in 0 plies obtained in AC/DC and MSC.Patran 12