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Fracture mechanics

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.

Fracture mechanics concepts

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

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.

If the material fails ductilely, that is 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 β€œcrack tip opening displacement”).

Relevant standards for fracture mechanics

  • ASTM E399-09 - Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness K1C of Metallic Materials
  • ASTM E647 – Standard Test Method for Measurement of Fatigue Crack Growth Rates (da/dN)
  • ASTM E1820-11 – Standard Test Method for Measurement of Fracture Toughness (metals)
  • ISO 12135 - Unified Method of Test for the Determination of quasistatic fracture toughness

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:

  • Region I:Threshold value Ξ”Kth
  • Region II:Fatigue crack growth da/dN
  • Region III:Critical stressing intensity factor K1C (fracture toughness)

Specimen shapes in fracture mechanics

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

More information on fracture mechanics

Testing Machines for Determination of Fracture Mechanics