Impact Damage Analysis of Composite Materials
Theory and Physics
Composite Material Impact Damage
Professor, what happens when composite materials are impacted?
Metals dent (plastic deformation) upon impact, but composite materials experience internal damage propagation. While there may be almost no visible trace on the surface, extensive internal matrix cracking, delamination, and fiber breakage occur internally.
That's BVID (Barely Visible Impact Damage), right?
Correct. In aircraft design, BVID (Barely Visible Impact Damage, difficult to detect visually) is the most stringent design condition. BVID occurs from tool drops (low-velocity impact), and the residual strength under compressive load after impact (CAI) determines the design allowable value.
Impact Classification
| Type | Velocity | Example | Primary Damage |
|---|---|---|---|
| Low-Velocity Impact | < 10 m/s | Tool drop, hailstone | Matrix cracking, delamination |
| Medium-Velocity Impact | 10〜100 m/s | Runway debris, bird strike | Penetration damage, extensive delamination |
| High-Velocity Impact | > 100 m/s | Ballistic impact | Penetration, plug formation |
| Hyper-Velocity Impact | > 1000 m/s | Space debris | Cratering, complete destruction |
Low-velocity impact is the most common and the cause of BVID, right?
Low-velocity impact occurs most frequently during aircraft operation. Design assumes BVID for impacts of specific energy (e.g., 35 J/Boeing, 50 J/Airbus) based on ICAO/FAA regulations.
Impact Damage Mechanism
Low-velocity impact damage mechanism (chronological):
1. Contact Initiation — Impactor contacts the plate
2. Matrix Cracking Initiation — Cracks form in orthogonal directions due to bending stress
3. Delamination Propagation — Matrix cracks reach the interface, causing delamination
4. Fiber Breakage — If energy is high, fibers also break
5. Rebound — Impactor bounces back. Damage remains
So delamination starts from matrix cracks.
When a matrix crack reaches the interface, delamination occurs if the energy at the crack tip exceeds the interlaminar fracture toughness. Delamination preferentially occurs at interfaces with different fiber angles (e.g., 0°/90° interface).
FEM for Impact Analysis
Impact analysis typically uses the Explicit Method. In Abaqus/Explicit or LS-DYNA:
- Impactor — Rigid or elastic body
- Plate — Solid elements + Hashin damage + CZM (interlaminar)
- Contact — General Contact or Penalty method
Do we need to include CZM for all layers?
Ideally yes, but computational cost becomes enormous. Placing CZM only at critical interfaces (where fiber angle changes abruptly) is practical.
Summary
Let me summarize the theory of composite material impact damage.
Key points:
- BVID — Internal damage invisible from the surface. The most stringent condition in aircraft design
- Damage Chain — Matrix cracking → delamination → fiber breakage
- Low-velocity impact is most common — Tool drops, hail, runway debris
- Simulate with Explicit Method — Hashin + CZM
- Delamination preferentially occurs at interfaces with abrupt fiber angle changes
Bird Strike Testing and the History of CFRP Impact Design
Bird strike testing for CFRP structures in aircraft is mandated by US FAR 25.571, assuming a 1.8kg bird impact at 270km/h. When CFRP began to be used in the 1970s, its impact characteristics were considered significantly inferior to metals. However, through laminate design optimization and impact after strength (CAI: Compression After Impact) optimization, it has been demonstrated that the current A350 wing has superior impact resistance compared to aluminum.
Physical Meaning of Each Term
- Inertia Term (Mass Term): $\rho \ddot{u}$, i.e., "mass × acceleration". Have you ever experienced being thrown forward during sudden braking? That "feeling of being carried away" is precisely the inertial force. Heavier objects are harder to set in motion and harder to stop once moving. Buildings shake during earthquakes because the ground moves suddenly while the building's mass "gets left behind". In static analysis, this term is set to zero, assuming "forces are applied slowly enough to ignore acceleration". It absolutely cannot be omitted in impact loading or vibration problems.
- Stiffness Term (Elastic Restoring Force): $Ku$ or $\nabla \cdot \sigma$. When you stretch a spring, you feel a "force trying to return it", right? That's Hooke's law $F=kx$, the essence of the stiffness term. Now a question — an iron rod and a rubber band, which stretches more under the same force? Obviously the rubber band. This "resistance to stretching" is the Young's modulus $E$, which determines stiffness. A common misconception: "high stiffness ≠ strong". Stiffness is "resistance to deformation", strength is "resistance to failure" — they are different concepts.
- External Force Term (Load Term): Body force $f_b$ (e.g., gravity) and surface force $f_s$ (e.g., pressure, contact force). Think of it this way — the weight of a truck on a bridge is a "force acting on the entire volume" (body force), while the force of the tires pressing on the road is a "force acting only on the surface" (surface force). Wind pressure, water pressure, bolt tightening force... all are external forces. A common mistake here: getting the load direction wrong. Intending "tension" but it becomes "compression" — sounds like a joke, but it actually happens when coordinate systems are rotated in 3D space.
- Damping Term: Rayleigh damping $C\dot{u} = (\alpha M + \beta K)\dot{u}$. Try plucking a guitar string. Does the sound continue forever? No, it gradually fades. That's because vibrational energy is converted to heat by air resistance and internal friction in the string. Car shock absorbers work on the same principle — intentionally absorbing vibrational energy to improve ride comfort. What if damping were zero? Buildings would continue shaking forever after an earthquake. Since that doesn't happen in reality, setting appropriate damping is crucial.
Assumptions and Applicability Limits
- Continuum assumption: Treats material as a continuous medium, ignoring microscopic heterogeneity
- Small deformation assumption (for linear analysis): Deformation is sufficiently small compared to initial dimensions, stress-strain relationship is linear
- Isotropic material (unless otherwise specified): Material properties are independent of direction (anisotropic materials require separate tensor definition)
- Quasi-static assumption (for static analysis): Ignores inertial/damping forces, considers only equilibrium between external and internal forces
- Non-applicable cases: Large deformation/large rotation problems require geometric nonlinearity. Nonlinear material behavior like plasticity or creep requires constitutive law extension
Dimensional Analysis and Unit Systems
| Variable | SI Unit | Notes / Conversion Memo |
|---|---|---|
| Displacement $u$ | m (meter) | When inputting in mm, unify loads/elastic modulus to MPa/N system |
| Stress $\sigma$ | Pa (Pascal) = N/m² | MPa = 10⁶ Pa. Note unit inconsistency when comparing with yield stress |
| Strain $\varepsilon$ | Dimensionless (m/m) | Note distinction between engineering strain and logarithmic strain (for large deformation) |
| Elastic Modulus $E$ | Pa | Steel: ~210 GPa, Aluminum: ~70 GPa. Note temperature dependence |
| Density $\rho$ | kg/m³ | In mm system: tonne/mm³ (= 10⁻⁹ tonne/mm³ for steel) |
| Force $F$ | N (Newton) | Unify as N in mm system, N in m system |
Numerical Methods and Implementation
FEM Model for Impact Analysis
Please tell me the specific settings for impact analysis.
Typical low-velocity impact model in Abaqus/Explicit:
Model Configuration
- Impactor: Rigid sphere (radius 12.5 mm, mass 3 kg, initial velocity 5 m/s → energy 37.5 J)
- Plate: Solid elements (C3D8R). Each layer 0.125 mm. 24 layers = 3 mm thickness
- CZM: Cohesive elements (COH3D8) placed at critical interfaces
- Contact: General Contact (automatic full-surface contact)
Mesh
- Around impact point: 0.5〜1 mm elements
- Remote areas: 2〜5 mm elements
- Through-thickness direction: 1 element per layer (solid) + CZM between layers
24 layers with 1 element each and CZM for all layers... that's a huge number of elements.
For a 20×20 mm refined zone around the impact area, it's about 500,000 elements. Computation time ranges from several hours to one day (can be accelerated with GPU).
Damage Evaluation
Result verification items:
- Force-Time Curve — Time history of contact force on the impactor. Peak force and contact duration
- Energy-Time Curve — Absorbed energy. Calculation of coefficient of restitution
- Damage Area — Projected area of delamination. Comparison with C-scan
- Damage Variables per Layer — Contours of Hashin's $d_{ft}, d_{mt}$
Comparing the damage area with C-scan is the key for validation, right?
Yes. If the FEM delamination area and the ultrasonic C-scan delamination area agree within 30%, the prediction is considered good. The shape (elliptical or peanut-shaped) is also compared.
Summary
Let me organize the numerical methods for impact analysis.
Key points:
- Abaqus/Explicit + C3D8R + Hashin + CZM — Standard configuration
- 1 element per layer + CZM between layers — Detailed model
- Verify with force-time, energy-time curves — Compare with experiment
- Compare damage area — FEM vs. C-scan. Good if within 30%
- High computational cost — 500k elements. Consider GPU utilization
CAI (Compression After Impact) Evaluation Procedure
CAI (Compression After Impact) is one of the most important characteristics in CFRP design. ASTM D7137 specifies impact with a 16mm diameter indenter at a specific energy (6.7J/mm), followed by compression testing of the same specimen to measure residual strength. CAI curves are obtained by varying impact energy, confirming that CAI at barely visible impact damage (BVID) exceeds the allowable compressive strength.
Linear Elements (1st Order Elements)
Linear interpolation between nodes. Low computational cost but lower stress accuracy. Beware of shear locking (mitigated with reduced integration or B-bar method).
Quadratic Elements (with Midside Nodes)
Can represent curved deformation. Stress accuracy improves significantly, but degrees of freedom increase by about 2-3 times. Recommended: when stress evaluation is critical.
Full Integration vs Reduced Integration
Full integration uses the minimum number of integration points required for accurate stiffness matrix integration. Reduced integration uses fewer points, reducing computational cost and mitigating shear locking but may introduce hourglass modes.
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