# Fracture mechanics (LEFM, YFM)

Linear-elastic fracture mechanics (LEFM), yielding fracture mechanics (YFM)

Fracture mechanics examines crack growth, crack propagation, and crack arrestability in a component or material under operating conditions (function, fatigue life, ...). The determined material characteristics, taking into consideration the stress-time function, influence the design and production of a component.

Fracture mechanics plays a major role in many industrial sectors such as aerospace or automotive engineering. By estimating the lifetime or remaining useful life of crack-affected components (or materials), inspection and maintenance intervals can be defined in a targeted manner.

A distinction is made between two concepts: linear-elastic fracture mechanics (LEFM) and yielding fracture mechanics (YFM).

## Linear-elastic fracture mechanics (LEFM)

In linear-elastic fracture mechanics (suitable for brittle materials), the material behavior is linear elastic until deformation-free fracture (unstable crack propagation) occurs. A classic characteristic value of LEFM is K1C, which describes the critical (C) stress intensity (K) during crack opening mode 1.

## Yielding fracture mechanics (YFM)

If the material failure is ductile, that is, it occurs with plastic deformation at the crack tip, then the yielding fracture mechanics concept is applied. There are two definitions here, one is the determination of the characteristic values via the energy stored in the crack tip environment (J-integral concept) and the other is via the crack tip expansion (CTOD “crack tip opening displacement”).

## Relevant Standards

Fracture mechanics: crack growth da/dN and threshold value
ASTM E647
to Fracture mechanics: crack growth da/dN and threshold value
Fracture mechanics: critical stress intensity factor K1C
ASTM E399
to Fracture mechanics: critical stress intensity factor K1C

## Crack propagation in metallic components

Production-related defects in the component or on the component surface, which every component has, represent crack nuclei that promote the formation of cracks under load. These defects can turn into a crack, i.e. macroscopic material damage that can be technically recorded. This is referred to as the crack initiation phase.

In the subsequent crack propagation phase, the crack continues in the component until the stress intensity K in front of the crack tip exceeds a critical value and the component fails abruptly.

Cracks propagate stably (pre-critical state) or unstably (critical state) in monotonically or cyclically loaded components. For brittle materials, the critical stress magnitude K1C can be specified, the determination of which is described in ASTM E399. If the stress intensity K of the growing crack moves below K1C, the crack propagates stably and can be stopped at any time when the load is removed. If the K1C value is exceeded, unstable crack growth will occur and the component will fail abruptly.

The crack growth curve can be divided into three regions:

## Specimen shapes

In fracture mechanics, different specimen shapes are used. The shapes are selected depending on the standard and the available material to be tested. Standardized specimen shapes are described in the standard to make the test results comparable.

### C(T) specimen

The specimen shape used most in fracture mechanics is the compact tension specimen. It used for testing to ASTM E399 / E647.

Further specimen shapes are also listed in the standards. They are each selected depending on the industry and available raw materials:

• M(T) specimen - Middle tension specimen for testing to ASTM E647
• ESE(T) specimen - Eccentrically loaded single edge crack tension specimen for testing to ASTM E647
• SE(B) specimen - Single-edge bend specimen for testing to ASTM E399
• DC(T) specimen - Disc-shaped compact tension specimen for testing to ASTM E399
• A(T) specimen - Arc-shaped tension specimen for testing to ASTM E399
• A(B) specimen - Arc-shaped bend specimen for testing to ASTM E399

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