For information, contact Heather Hickman at heather.k.hickman@nasa.gov.

Background 

LEFM methods have traditionally been used to successfully 

characterize the damage tolerance life of elastically responding 

components that contain cracks that are small relative to the 

thickness or other structural features. However, prediction of partthrough cracks in thin metallic materials, where break-through is an 

end-of-life condition (e.g., COPV liners or thin metal pressure vessels), 

presents a unique problem. For example, traditional plastic zone 

limits that bound the use of LEFM (e.g., Irwin plastic zone model) are 

based on cracks in semi-infinite bodies and can be unconservative 

for a part-through crack approaching the back surface of a thin 

component. Furthermore, existing standards (e.g., ANSI/AIAA S-081 

and S-080) do not provide guidelines for end-of-life limits in damage 

tolerance life analysis with LEFM tools such as NASGRO.

Discussion

In addressing the impact of LEFM plasticity assumptions on 

conservatism of damage tolerance life predictions, the NESC 

assessment team:

• Performed testing to generate crack growth and crack mouth 

opening displacement (CMOD) data.

• Performed LEFM analyses using NASGRO v8.2 as an exemplar 

LEFM tool to compare against crack growth test data.

• Developed a validated finite element model (FEM) to compare 

predicted crack behavior using elastic and elastic-plastic 

material models (Figure 1).

• Experimentally and numerically demonstrated that the divergence between elastic and elastic-plastic predictions is gradual.

The validated FEM considered various crack sizes, liner thicknesses, 

stress levels, and materials. Analysis data demonstrated a gradual 

divergence in predicted elastic-plastic and elastic crack behavior. As 

a result, the NESC assessment team:

• Developed criteria that expands on the concepts developed in 

ASTM E2899 to determine when LEFM plasticity assumptions 

are invalid (i.e., LEFM limit, aL).

• Provided a modified failure criterion, ai*, to be considered 

when LEFM analyses are used beyond the LEFM limit.

As illustrated in Figure 2, ai* is a knockdown on the LEFM damage 

tolerance life state-of-practice limit (i.e., the Irwin plastic zone limit, 

ai), meaning ai* is as or more conservative than ai. To account 

for the aforementioned gradual divergence between elastic and 

elastic-plastic predictions, the knockdown is only applied when the 

analysis shows exceedance of the LEFM limit, aL. The magnitude 

of the knockdown depends on the degree of exceedance, elasticplastic finite element analysis, and applicable test data. 

LEFM Evaluation Approach

When LEFM-based fatigue crack growth predictions are made for 

damage tolerance life (e.g., with a LEFM tool such as NASGRO), 

COPV and metal pressure vessel designers should use the following 

analysis procedure to address the potential violation of LEFM 

plasticity assumptions:

• Simulate crack growth to failure (i.e., breakthrough).

• Identify the predicted crack depth after 4-lifetimes, aF.

• Identify the limits ai, aL, and ai*.

• Verify that aF <ai*, otherwise the design does not meet 

recommended requirement for damage tolerance life by analysis.

• Report aF, ai, aL, and ai* to fracture control engineering 

technical authority.

References

1. ANSI/AIAA-S-081 and ANSI/AIAA-S-080, Space Systems – 

Composite Overwrapped Pressure Vessels, Metallic Pressure 

Vessels, Pressurized Structures, and Pressure Components

2. COPV Damage Tolerance Life Analysis and Test Best 

Practices, NASA/TM-2020-5006765 

3. Damage Tolerance Life Issues in COPVs with Thin Liners, 

NESC-TB-16-02

Evaluating Appropriateness of LEFM Tools for COPV and Metal 

Pressure Vessel Damage Tolerance Life Verification

Human spaceflight composite overwrapped pressure vessels (COPVs) and metal pressure vessels can use linear elastic fracture mechanics 

(LEFM) analysis to demonstrate damage tolerance life in some cases per ANSI/AIAA-S-081 for COPVs and ANSI/AIAA-S-080 for metal 

pressure vessels. LEFM analysis assumptions require that the crack tip plastic zone is small relative to the crack size and is completely 

surrounded by elastically responding material. Test and analysis have shown that LEFM tools (e.g., NASGRO*) can provide unconservative 

crack growth predictions for cracks in COPV liners that violate LEFM assumptions. COPV and metal pressure vessel designers should 

evaluate and address the violation of LEFM plasticity assumptions before using LEFM analysis tools for damage tolerance life verification.

NASA Engineering and Safety Center Technical Bulletin No. 21-04

National Aeronautics and Space Administration

www.nasa.gov

07/30/21

Figure 1. Plastic zone size from FEM comparing LEFM limit calculated according to 

ASTM E2899-15 and the Irwin limit. The crack tip plastic zone is highlighted in red.

Back Face 

Plasticity

Figure 2. Schematic of a surface crack growth simulation and applicable limits on a, 

including the Irwin limit, ai, the LEFM limit, aL, and the modification limit, ai*.

Initial Crack

W a=B

a=ai

a=aL

ai*

Crack progression defined 

by LEFM simulation

Acceptable analysis 

( a < ai* )

B

*NASA retains a royalty-free license to use NASGRO for NASA purposes, including use by NASA contractors on NASA projects.