Surface Ply Damage

Surface Ply Damage 1

SURFACE PLY DAMAGE

1 INTRODUCTION

Surface ply damage is simulated by the removal of one ply. This could be the first or last ply of the laminate depending on the configuration of the structure. In this analysis, all the plies of a given laminate are assessed for the impact of the loss of effectiveness of one ply.

Surface ply damage methodology is presented in Section 2, based on Tsai- Hill Failure Index. However, any failure criterion maybe applied. All the applied and allowable stresses are given in the material (ply) axes system (1,2) as presented in Figure 1. An element Failure Index in that of its critical ply Failure Index. An example showing how to use this PATRAN Command Language (PCL) Function is presented in Section 3. Surface Ply Damage 2

MATERIAL (PLY) AXES SYSTEM (0°)

0°/90° 2 LAMINATE AXES 1 SYSTEM y

MATERIAL (PLY) AXES SYSTEM (+45°)

45°

2 LAMINATE 1 AXES y SYSTEM

Figure 1. Material (ply), and laminate axes systems – 1,2 and x,y respectively. Ply applied and allowable stresses are given in the material (ply) axes system.

Surface ply damage analysis methodology is given next. Surface Ply Damage 3

2 SURFACE PLY DAMAGE

Surface ply damage is simulated by the removal of one ply. This could be the first or last ply of the laminate depending on the configuration of the structure. In this analysis, all the plies of a given laminate are assessed for the impact of the loss of effectiveness of one ply. Surface ply damage analysis procedure is shown in Figure 2. A PCL function is used for this analysis, activated by running a session file with the appropriate input data. The next section deals with the ply applied stresses.

2.1 APPLIED STRESS

Element ply-by-ply applied stresses in the material (ply) axes system (1,2) – see Figure 1 – are extracted from PATRAN database. The applied ply stresses are given as follows:

1  applied stress in direction 1

 2  applied stress in direction 2

12  applied shear stress in plane 1,2

The allowable stresses are addressed next.

2.2 ALLOWABLE STRESS

At a given operating temperature, ply allowable stresses in the material axes system (1,2) – see Figure 1 – are used to calculate the surface ply damage Tsai-Hill Failure Index. The allowable stresses are given as follows:

S1_TENS = allowable tensile strength in direction 1 S1_COMP = allowable compressive strength in direction 1 S2_TENS = allowable tensile strength in direction 2 S2_COMP = allowable compressive strength in direction 2 S12 = allowable shear strength in plane 1,2

The next section addresses the stress factor due to surface ply damage. Surface Ply Damage 4

2.3 STRESS FACTOR

Surface ply damage Stress Factor (SF) is given by Eq. 1 as:

AS DESIGNED LAMINATE THICKNESS STRESS FACTOR (SF)  Eq. 1 DAMAGED LAMINTE THICKNESS

Where, the ‘damaged’ laminate thickness corresponds to the removal of one ply. This could be the first or last ply of the laminate depending on the configuration of the structure. In this analysis, all the plies of the laminate are analysed for the impact of the loss of one ply. The next section deals with the Tsai-Hill Failure Index.

2.4 TSAI-HILL FAILURE INDEX

The ply Tsai-Hill Failure Index for surface ply damage analysis is given by the following equation, which accounts for the surface ply damage stress factor:

2 2 2 (1  SF) (1  SF)  ( 2  SF) ( 2  SF) (12  SF) Eq. 2 FI  2  2  2  2 S1 S1 S2 S12

Where,

S1  allowable tensile S1_ TENS or compressive S1_ COMP strength in direction 1

S2  allowable tensile S2 _ TENS or compressive S2_ COMP strength in direction 2

S12  allowable shear strength in plane 1,2

If 1 is tensile, S1  S1_ TENS

If 1 is compressive, S1  S1_ COMP

If  2 is tensile, S2  S2 _ TENS

If  2 is compressive, S2  S2 _ COMP

Or, re-written as:

2 2 2 (1  SF)  (1  SF)  ( 2  SF) ( 2  SF) (12  SF) Eq. 3 FI  2  2  2 S1 S2 S12 Surface Ply Damage 5

The maximum Failure Index of an element corresponds to its maximum ply Failure Index. This Failure Index is displayed in PATRAN output for the element. Surface Ply Damage 6

SURFACE PLY DAMAGE ANALYSIS: INPUT TO PCL FUNCTION 1) PATRAN group name (PCOMP at a given temperature) Load case name Sub case name Results coordinate system Number of layers of laminate Layer thickness Allowable ply tensile stress in direction 1 S 1_TENS Allowable ply compressive stress in direction 1 S 1_COMP Allowable ply tensile stress in direction 2 S 2_TENS Allowable ply compressive stress in direction 2 S 2_COMP Allowable ply shear stress in plane 1,2 S 12

CALCULATE STRESS FACTOR (SF) 2) EXTRACT APPLIED STRESSES 2) ‘Damaged’ laminate: one ply removed For each element, extract from PATRAN database ply direct and shear stresses in the material (ply) axes system 1,2

CALCULATE PLY TSAI-HILL FAILURE INDEX (FI) 2) For each ply of each element to include the effect of surface ply damage Stress Factor

CREATE NEW RESULT CASE: PLY-BY-PLY FAILURE INDEX 2) Create a new result case for each ply and add to PATRAN database

DETERMINE ELEMENT FAILURE INDEX 3) Each element is attributed its maximum ply Failure Index 4)

PLOT FAILUER INDEX 3) Element-by-element plot 5)

Notes: 1) .ses file; 2) .pcl file; 3) .db file; 4) Results/Create/Results/Maximum (max of same ply numbers; then max of all plies); 5) Results/Create/Fringe

Figure 2. Surface ply damage analysis procedure. Surface Ply Damage 7

3 EXAMPLE

A finite element model of a cantilevered section, built-in at its root, is shown in Figure 3. It consists of three composite regions as given in Table 1. Unit pressure loading is applied on the surface of the elements. Table gives the allowable stresses in the material (ply) axes system (1,2) – see Figure 1. All the applied ply stresses are in material (ply) axes system (1,2) as shown in Figure 1.

Table 2 shows laminate details. Allowable stresses in the material (ply) axes system (1,2) are given in Table 3. Figure 4 shows the deformed shape. The Tsai-Hill Failure Indices are presented in Figure 5 to Figure 7.

BUILT-IN EDGE

Prop1_region Prop2_region Prop3_region

Figure 3. Finite element mesh. Surface Ply Damage 8

Table 2. Laminate details.

Regions 1 to 3 Ply Area Lay-up No. PCOMP Thickness of (mm) Plies Prop_prop1_region 0.25 Tip 45/-45/-45/45 4 Prop_prop2_region 0.25 Mid-section 45/0/-45/-45/0/45 6 Prop_prop3_region 0.25 Root 45/0/90/-45/-45/90/0/45 8

Table 3. Allowable stresses in the material (ply) axes system (1,2).

Allowable Stresses in the Material (Ply) Axes System (1,2) Allowable Allowable Allowable Allowable Allowable Tensile Compressive Tensile Compressive Shear Stress in Stress in Stress in Stress in Stress in Direction 1 Direction 1 Direction 2 Direction 2 Plane 1,2

S1_TENS S1_COMP S2_TENS S2_COMP S12 (MPa) (MPa) (MPa) (MPa) (MPa) 1500 1000 50 200 150 Surface Ply Damage 9

Figure 4. Deformed shape.

Figure 5. Surface ply damage analysis (one ply removed) maximum Tsai-Hill Failure Indices (all plies 1 to 6). The maximum Failure Index is 0.90, occurring at element 56 (PCOMP prop_prop3_region: root). Surface Ply Damage 10

Figure 6. Surface ply damage analysis (one ply removed) maximum Tsai-Hill Failure Indices (ply 7: 0). The maximum Failure Index is 0.44, occurring at element 56 (PCOMP prop_prop3_region: root).

Figure 7. Surface ply damage analysis (one ply removed) maximum Tsai-Hill Failure Indices (ply 8: 45). The maximum Failure Index is 0.67, occurring at element 56 (PCOMP prop_prop3_region: root). Surface Ply Damage 11

3.1 FILES USED

The files used are given in Table 4. Files interaction is presented in Figure 8.

Table 4. Files used.

.bdf File surface_ply_damage.bdf .ses File surface_ply_damage.ses .pcl File surface_ply_damage.pcl Surface Ply Damage 12

.bdf FILE Create a SET of elements of all PCOMPs Run .bdf file, requesting STRESS output for the above SET

.db FILE Create a database by reading in the above .bdf file into an empty database (File/Import/Model/MSC NASTRAN Input) Read in .xdb file Create property groups for all PCOMPs (Utilities/Group/Groups From Properties)

.ses FILE .pcl FILE Specify directory of .pcl file Performs analysis Input data required by PCL function Creates a new result case (Failure Index) for Run session file to activate PCL function each ply and adds to PATRAN database (File/Session/Play)

Figure 8. Files interaction.