Extended CTOD Concept

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Extended CTOD concept

Critical crack opening displacement δ

The fracture mechanical parameter crack opening displacement δ (see: crack opening), determined according to the crack tip opening displacement concept (CTOD), is suitable for describing the deformability of materials. In the case of a three-point bending test specimen, the determining Eq. (1) for δ is:

$\delta ={\frac {1}{n}}(W-a){\frac {4\ f_{max}}{s}}$

(1)

with

n		rotation factor
W		test specimen with
a		notch depth (initial crack length)
fmax		maximum deflection
s		support span (see support distance)

Crack opening displacement δ is always useful when material users or developers are looking for a parameter that clearly describes increasing embrittlement (see:brittle fracture promoting factors) and represents a geometry-independent variable (see: geometry criterion).

Deflection splitting

Assuming [1] that the experimentally measured test specimens deflection f_max can be calculated from the deflection of the unnotched part f_B and the part caused by the deformation in the area of the notch f_K (notch part) according to Eq. (2)

$f_{max}=f_{K}+f_{B}\!$

(2)

where the bending portion f_B is calculated using Eq. (3)

$f_{B}={\frac {F_{max}\ s^{3}}{4\ E\ B\ W^{3}}}$

(3)

with E = modulus of elasticity, the relationship between deflection and the a/W ratio can be interpreted. When using the critical crack opening δ, it is therefore possible to separate the influence of pure bending in the form of the deflection part and the notch part.

Application of the extended CTOD concept for polypropylene (PP), polyamide (PA) and chlorinated polyvinyl chloride (PVCC)

Figure 1 shows that the bending part decreases as the a/W ratio increases, i.e. at a/W = 0.1 it accounts for 40 % of the total deflection and at a/W = 0.7 only 5 %. For high notch depths, the f_K part dominates [2].

Fig. 1:

Deflection parts fmax, fK and fB at the beginning of unstable crack propagation for PP [2]

Fig. 2:

Deflection parts fmax, fK and fB at the beginning of unstable crack propagation for polyamide 6 and PVCC [2]

The fracture mechanics parameters δ_Id (calculated with f_max), δ_IdK (calculated with the notch part f_K) and δ_IdB (calculated with the bending part f_B) show a similar qualitative curve progression to the representations selected in Fig. 1 and Fig. 2.

See also

• Crack tip opening displacement concept (CTOD)
• Fracture mechanics
• Crack opening
• Plastic hinge model
• ICIT – Nonlinear material behaviour

References

[1]	Srawley, J. E.: Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens. International J. of Fracture Mechan. 12 (1976) 475–476 DOI: https://doi.org/10.1007/BF00032844
[2]	Grellmann, W.: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), Technische Hochschule Leuna-Merseburg, Wiss. Zeitschrift TH Merseburg 28 (1986) H. 6, S. 787‒788 (Inhaltsverzeichnis, Content, Summary)