Scope:

When a fast-running crack arrests, the stress intensity factor is a measure of the ability of the material to arrest such a crack. The stress intensity factor provides a value for the crack-arrest fracture toughness, K_A. ASTM E1221 test method provides a static analysis determination of the stress intensity factor in a short time after the crack arrest. The estimate is denoted as K_a. When certain size requirements are met, the test result provides an estimate, termed K_Ia, of the plane-strain crack-arrest toughness of the material. K_A cannot be determined if the specimen does not show rapid crack propagation and arrest. This test method is used in a material’s research and development and to determine the effects of metallurgical variables such as composition or heat treatment on the ability to arrest running cracks. 

Test Procedure:

ASTM E1221 method is used to calculate the stress intensity factor, K. In this test, a wedge is forced into a split-pin. This applies a force across the crack starter notch, provoking a run and arrest crack extension. This run-arrest crack propagation needs a dynamic analysis of the test results. However, an adjusted static analysis of test results provides a useful estimate of the stress intensity factor at the time of the crack arrest. K_A is determined from dynamic analysis; K_Ia is determined from static analysis. 

K₀ is the stress intensity factor, K, at the onset of crack propagation. 

Video 01: Method to measure fracture toughness

Specimen size:

• This ASTM E1221 test method uses a side-grooved, crack-line-wedge-loaded specimen to obtain a rapid run-arrest segment of flat-tensile separation with a nearly straight crack front. 

• The thickness should be either full product plate thickness or a thickness sufficient to produce a condition of plane strain. 

• Certain size requirements must be met to limit plastic deformation in the specimen before crack initiation. These requirements depend upon the material yield strength, and K_a and K₀ are needed to achieve an appropriate run-arrest event. 

• The in-plane specimen dimensions must be large enough to allow for the linear elastic analysis employed. 

• A starting notch should be machined that will permit crack propagation. Different materials require different starter notch preparation procedures. 

Data:

From the autographic force-displacement record, several displacement values are determined. 

The following data is calculated in ASTM E1221:

Calculation of K_A and K_Qa : 

Where:

E = Young’s modulus,

a = slot size,

W = specimen width, 

B = specimen thickness, 

B_N = specimen thickness at the crack plane, 

δ = crack mouth opening displacement, 

To calculate K₀, use a = a₀ and δ = d₀. 

To calculate K_a, use a = a_a and δ = d_a. 

The quantities d₀ and d_a are given as follows:

Young modulus: 

Y = (38.3 × f² × ρ × ℓ⁴)/d²

Y = Young’s Modulus

f = resonance frequency of oscillations.

ρ = density

ℓ = length

d = width

Conclusion:

ASTM E1221 test method provides a static analysis determination of the stress intensity factor in a short time after the crack arrest.