J-Compliance Method

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J-Compliance method

J-Integral evaluation method – Compliance method

J-integral evaluation methods are used for the determination of fracture mechanical values according to the J-integral concept [1].

The first proposal for the experimental determination of J_IC was made by Begley and Landes [2, 3] and is based on the energetic interpretation of the J-integral according to Rice in the following form:

$J_{I}=-{\frac {1}{B}}{\frac {\partial A}{\partial a}}$

This method is also referred to in the literature as the evaluation method according to BEGLEY and LANDES. Here it is called the J-compliance method for differentiation.

Implementation of the compliance method

The procedure of the J-compliance method is to be illustrated using the example of impact load (F)–deflection (f) diagrams recorded in the instrumented Charpy impact test (ICIT) (Fig. 1a to 1c).

To carry out the procedure, load–deflection diagrams (Fig. 1a) are recorded on several test specimens with different notch depths (in Fig. 1, this is limited to three test specimens). The energy A_G is determined by integrating the area under the F–f curve for certain f_i values and the ratio A_G/B is shown as a function of the crack length (notch depth) (Fig. 1b).

A graphical differentiation (Fig. 1c) of these curves yields J_I as a function of f_i, from which the critical J_Ic values can be obtained after measuring the deflection at the moment of unstable crack propagation.

Fig. 1:

Determination of J-integral according to the J-compliance method: a) load–deflection diagram, b) AG/B–notch depth diagram and c) J-integral–deflection diagram

Accuracy of the compliance method

In [1], J ^COM values determined using the J-compliance method on two plastics and J ^FEM values calculated using the finite element method (FEM) were compared as a function of the crack length. An overestimation of the toughness was found for the J ^COM values for small crack lengths and an underestimation of the toughness for a crack length (a)/specimen width (W) ratio of a/W > 0.2, which was attributed to an insufficient consideration of the limited specimen geometry. A significant disadvantage of this method is the high number of test specimens required.

See also

• J-integral concept
• ICIT ( Instrumented Charpy impact test)
• J-integral estimation methods of BEGLEY and LANDES (BL)

References

[1]	Grellmann, W.: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), Technische Hochschule Merseburg, Wiss. Zeitschrift TH Merseburg 28 (1986), H.6, p. 787–788
[2]	Begley, J. A., Landes, J. D: The J-Integral as a Failure Criterion. ASTM STP 514 (1972) p. 1–20
[3]	Landes, J. D., Begley, J. A.: The Effect of Specimen Geometry on JIc. ASTM STP 514 (1972) p. 24–39