Predicting Failure of Multiangle Composite Laminates

Predicting Failure of Multiangle Composite Laminates Preliminary discussion (not in textbook): Micromechanics failure analyses vs Macromechanics failure analyses

Fiber Architecture of Some Common Composite Forms Hayes, B.S., and Gammon, L.M., Optical Microscopy of Fiber-Reinforced Composites (2010)

Fiber Architecture of Some Common Composite Forms Shifman, T.J., Compression Molding Flow Effects on Material Properties for a Discontinuous Chopped Fiber Composite, UW MSME thesis (20)

Unit Cells Used in Micromechanic FEM Analyses Hyer, M.W., Stress-Analysis of Fiber-Reinforced Composite Materials, McGraw-Hill (1998)

Micromechanics failure analyses: Are defined at a physical scale corresponding to the fiber diameter Help identify and explain the stress-strainenvironmental conditions that initiate cracks that (ultimately) lead to failure Guide the development of new/improved composite materials Are too computationally intensive to be useful during engineering design of a composite structure Macromechanics failure analyses: Are based on a smearing assumption a ply is treated as a homogeneous anisotropic material Are based on failure properties measured at a physical scale corresponding to the ply thickness: ε,, ε fc fc,, ε,, ε Are typically used during engineering design but cannot capture the details of crack initiation at the micro level, γ, τ f 12 f 12

Figure 7.1: Idealized stress-strain plot for a [0/45/90/-45] 2 laminate, showing evolution of internal damage

Damage Evolution During Uniaxial Tension-Tension Fatigue Loading Reifsnider et al (VA Tech, ~1985) Fatigue Loading: N max min avg = 0.2 = 0.02 = 0.34 ult ult ult = 70,000 cycles R = 0.1

Figure 7.1: Idealized stress-strain plot for a [0/45/90/-45] 2 laminate, showing evolution of internal damage

(Figure 7.2: Summary of First-ply Failure Calculations)

Example Problem 7.1 [0/30/0] s graphite-epoxy laminate Properties from Table 3.1 Cured at 175ºC, cooled to 20ºC ( T = -155ºC) Uniaxial tensile load N xx applied Predict first-ply failure load, based on Max Stress failure criterion As per Figure 7.2, for each ply: Calculate stresses (,, τ 12 ) caused by T only Calculate stresses (,, τ 12 ) caused by unit load (N xx = 1 N/m) only

Stresses in 0º ply: τ 12 = ( 2750) N xx 55. 54x10 = ( 51. 93 ) N xx + 28. 3 x 10 = ( 174. 8) Nxx +. 83x10 Stresses in 30º ply: 12 29 59 10 = ( ) Nxx +. x 120 24 79 10 = (. ) Nxx +. x τ12 = ( 24. ) Nxx + 0 Stresses in 0º ply: τ = ( 209. 8) Nxx 55. 54x10 = ( 17. 0) Nxx + 28. 3x10 12 = ( 89. 85) Nxx. 83x10

Maximum stress failure criterion: For 0º ply: N N N xx xx xx fc 1* < < fc 1* < < = ( 2750) N = f τ 12 < τ 12 xx 55. 54x10 + 55. 54x10 2750 1500x10 + 55. 54x10 = 2750 = 55, 727N / m <

Maximum stress failure criterion: For 0º ply: N N N xx xx xx fc 1* < < fc 1* < < = ( 51. 93) N = f τ 12 < τ 12 xx 51. 93 + 28. 3x10 28. 3x10 50x10 28. 3x10 = 51. 93 = 41. 715N / m <

Maximum stress failure criterion: For 0º ply: τ 12 N N N xx xx xx fc 1* < < fc 1* < < = ( 174. 8) N τ = f 12 f τ 12 < τ 12 xx 174. 8 +. 83x10. 83x10 < τ f 12 ± 75x10 28. 3x10 = 174. 8 = ( 2, 819N / m), ( 591, 304N / m)

Maximum stress failure criterion: fc 1* < < fc 1* < < f τ 12 < τ 12 For tensile N xx, 0º ply will fail if: N N xx xx (select): = 41. 7kN = 41. 7kN / / m, 55. 7kN/m, 591. 3kN m / m

Repeating this process for the 30º and 0º plies completes Table 7.1:. first ply failure is predicted to occur in the 0º plies at N xx = 123 kn/m.

Comparable approach can be used with Tsai-Hill or Tsai-Wu Criterion: Tsai-Hill failure criterion ( ) 2 + ( ) 2 ( τ ) ( ) 2 ( ) 2 ( f ) 2 ( ) τ + 12 12 2 2 < 1 Tsai-Wu failure criterion X 1 + X 2 + + X X 2 12 τ 2 + + X 2 2 X 12 < 1 As before, for 0º plies: τ 12 = ( 2750) N xx = ( 51. 93) N xx 55. 54x10 + 28. 3x10 = ( 174. 8) Nxx +. 83x10 Substitute the 0º ply stresses into selected FC and solve for N xx

Example Problem 7.1 Reconsidered [0/30/0] s graphite-epoxy laminate Properties from Table 3.1 Cured at 175ºC, cooled to 20ºC ( T = -155ºC) Uniaxial tensile load N xx applied Predict first-ply failure load, based on: Predict first-ply failure load, based on: - Max Stress failure criterion - Tsai-Hill failure criterion - Tsai-Hill failure criterion

Example Problem 7.1 Reconsidered [0/30/0] s graphite-epoxy laminate Properties from Table 3.1 Cured at 175ºC, cooled to 20ºC ( T = -155ºC) Uniaxial tensile load N xx applied Predict first-ply failure load, based on: - Max Stress failure criterion - Tsai-Hill failure criterion - Tsai-Hill failure criterion Results: Max Stress: 0º ply fails at N xx = 123 kn/m

Example Problem 7.1 Reconsidered [0/30/0] s graphite-epoxy laminate Properties from Table 3.1 Cured at 175ºC, cooled to 20ºC ( T = -155ºC) Uniaxial tensile load N xx applied Predict first-ply failure load, based on: - Max Stress failure criterion - Tsai-Hill failure criterion - Tsai-Hill failure criterion Results: Max Stress: 0º ply fails at N xx = 123 kn/m Tsai-Hill: 0º ply fails at N xx = 103 kn/m

Example Problem 7.1 Reconsidered [0/30/0] s graphite-epoxy laminate Properties from Table 3.1 Cured at 175ºC, cooled to 20ºC ( T = -155ºC) Uniaxial tensile load N xx applied Predict first-ply failure load, based on: - Max Stress failure criterion - Tsai-Hill failure criterion - Tsai-Hill failure criterion Results: Max Stress: 0º ply fails at N xx = 123 kn/m Tsai-Hill: 0º ply fails at N xx = 103 kn/m Tsai-Wu: 0º ply fails at N xx = 89.9 kn/m

Program LAMFAIL Performs first-ply failure analyses User selects one of three failure criterion: Maximum Stress Tsai-Hill Tsai-Wu Can predict: Failure for specified combination of unit stress or moment resultants, T, and M (as in Example Prob 7.1) ****or**** Generate data points that can subsequently be used to create a firstply failure envelope (sec 7.4)

Failure envelopes are analogous to yield (or fracture) surfaces for plane stress, typically discussed for isotropic materials: (taken from Dowling, N.E., Mechanical Behavior of Materials, Prentice Hall, 1998) Note: Yielding or fracture of isotropic materials governed by principal stresses not true for anisotropic composites

LAMFAIL can be used to create firstply failure envelope based on any two of the six resultants:

Figure 7.1: Idealized stress-strain plot for a [0/45/90/-45] 2 laminate, showing evolution of internal damage

Last-ply failure predictions can be made using the ply discount scheme a rudimentary method of predicting damage accumulation Summarized in Figure 7.3: Specify problem (including loads and failure criterion) Use CLT and selected failure criterion to determine first ply failure load Discount stiffnesses of failed ply(ies) Use CLT and reduced material properties to determine next ply(ies) to fail...reduce properties of newly-failed plies Repeat until all plies are predicted to have failed, at which point the Last-Ply Failure Load has been predicted

(Figure 7.3: Summary of Last-ply Failure Calculations)

Program PROGDAM ( progressive damage ) can be used to calculate first and last ply failure loads for an individual monotonically-increasing stress or moment resultant (i.e., for N xx, N yy, N xy, M xx, M yy, or M xy ) Example Problem 7.3: Illustrates last-ply failure analysis for a [0/30/0] s Gr/Ep laminate subjected to uniaxial tensile stress xx = N xx / t assuming: E failed = E ν failed 12 = ν 12 E G failed failed 12 = = 0.30E 0.30G 12

Figure 7.4: Predicted stress-strain curve for a [0/30/0]s graphite-epoxy laminate, based on the ply-discount scheme

Second example: last-ply failure analysis for a [0/45/90/-45] s Gr/Ep laminate subjected to M xx ( pure bending ), now assuming: E ν failed failed 12 = = 0.90E 0.90ν 12 E failed = 0.30E G failed 12 = 0.30G 12

Moment Resultant M xx (N-m/m) 350 300 250 200 150 100 50 0 Ply 7 fails (45º) Ply 8 fails (0º) Ply 5 fails (-45º) Ply fails (90º) Ply 3 (90º) and Ply 4 (-45º) fail simultaneously Ply 1 fails (0º) Ply 2 fails (45º) 0 10 20 30 40 50 Midplane Curvature κ xx (rad/m)

Advanced Damage Progression Models Program PROGDAM is a firstgeneration approach to predicting damage progression Current R&D efforts involve the use of advanced finite-element analyses, often with a stochastic (probabilistic) aspect Computationally expensive.

Advanced Damage Progression Models Typical example: Short course offered by University of Delaware (http://www.ccm.udel.edu/software/ mat12/mat12_workshop/): Progressive Composite Damage Modeling in LS-DYNA (MAT12 & Others) Progressive damage modeling of composites under low velocity impact, and high velocity impact is of interest to many applications including car crash, impact on pressure vessels, perforation and penetration of thin and thick section composites. This course will provide a comparison between available composite models in LS-DYNA for shell and solid elements, e.g., MAT2, MAT54, MAT59, & MAT12. Among these material models, rate dependent progressive composite damage model MAT12 is considered as the state of the art. This short course will include the theory and practice of MAT12 composite damage model with applications to low and intermediate impact velocities, understanding the LS-DYNA programming parameters related to impact-contact, damage evolution, perforation and penetration of thin- and thick-section composites. Printed copies of all lecture notes will be provided along with a CD containing all example LS- DYNA keyword input decks used in this short course.