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Oluschinski — Mon, 12 Oct 2026 08:10:27 GMT

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	*CRB-Test (Crack Round Bar Test) (see [[Full Notch Creep Test (FNCT)]] and [[Pennsylvania Edge Notch Tensile (PENT) Test]])		*CRB-Test (Crack Round Bar Test) (see [[Full Notch Creep Test (FNCT)]] and [[Pennsylvania Edge Notch Tensile (PENT) Test]])
	*[[Creep Behaviour – Creep Compression Test]]		*[[Creep Behaviour – Creep Compression Test]]
			*[[Creep Behaviour – Creep Internal Compression Test]]
	*[[Creep Behaviour – Determination]]		*[[Creep Behaviour – Determination]]
	*[[Creep Behaviour – Flexural Creep Test]]		*[[Creep Behaviour – Flexural Creep Test]]
	*[[Creep Behaviour – Creep Internal Compression Test]]
	*[[Creep Behaviour – Creep Compression Test]]
	*[[Creep Behaviour – Recovery Test]]		*[[Creep Behaviour – Recovery Test]]
	*[[Creep Behaviour – Tensile Creep Test]]		*[[Creep Behaviour – Tensile Creep Test]]
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	*Stress-Strain-Diagram (see [[Tensile Test]])		*Stress-Strain-Diagram (see [[Tensile Test]])
	*[[Stretch Zone]]		*[[Stretch Zone]]
	*[[SUMPTER and TURNER – J-Integral Estimation Method]] (ST) ~~– J-integral estimation method~~		*[[SUMPTER and TURNER – J-Integral Estimation Method]] (ST)
	*[[Support Distance]]		*[[Support Distance]]
	*Support Span (see [[Support Distance]])		*Support Span (see [[Support Distance]])
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	*Transverse Contraction (see [[Poisson's Ratio]])		*Transverse Contraction (see [[Poisson's Ratio]])
	*[[Trapezoidal Specimen]]		*[[Trapezoidal Specimen]]
	*Traverse Path Measurement (see [[Tensile Test]]m [[Compression Test]] and [[Bend Test]])		*Traverse Path Measurement (see [[Tensile Test]], [[Compression Test]] and [[Bend Test]])
	*Triaxial Loading (see [[Multiaxial Stress State]])		*Triaxial Loading (see [[Multiaxial Stress State]])
	*Tribological Stress (see [[Stress]])		*Tribological Stress (see [[Stress]])

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Oluschinski — Fri, 09 Oct 2026 11:06:45 GMT

← Older revision		Revision as of 13:06, 9 October 2026
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	<onlyinclude>__NOTOC__<div class="toc noprint" style="font-size: 1.2em; word-spacing: 0.8em; display:table; padding: 7px; border: 1px solid #a2a9b1; background-color: #f8f9fa; clear:left" role="navigation"><!-- Spezial:Diff/124689226 --><div><span style="font-weight:bold" lang="{{int:lang}}">{{int:toc}}</span> [[#A{{{1\|}}}\|A]] [[#B{{{1\|}}}\|B]] [[#C{{{1\|}}}\|C]] [[#D{{{1\|}}}\|D]] [[#E{{{1\|}}}\|E]] [[#F{{{1\|}}}\|F]] [[#G{{{1\|}}}\|G]] [[#H{{{1\|}}}\|H]] [[#I{{{1\|}}}\|I]] [[#J{{{1\|}}}\|J]] [[#K{{{1\|}}}\|K]] [[#L{{{1\|}}}\|L]] [[#M{{{1\|}}}\|M]] [[#N{{{1\|}}}\|N]] [[#O{{{1\|}}}\|O]] [[#P{{{1\|}}}\|P]] [[#Q{{{1\|}}}\|Q]] [[#R{{{1\|}}}\|R]] [[#S{{{1\|}}}\|S]] [[#T{{{1\|}}}\|T]] [[#U{{{1\|}}}\|U]] [[#V{{{1\|}}}\|V]] [[#W{{{1\|}}}\|W]] [[#Y{{{1\|}}}\|Y]] [[#Z{{{1\|}}}\|Z]] [[#Categories{{{1\|}}}\|Categories]] {{{2\|}}}</div></div></onlyinclude>		<onlyinclude>__NOTOC__<div class="toc noprint" style="font-size: 1.2em; word-spacing: 0.8em; display:table; padding: 7px; border: 1px solid #a2a9b1; background-color: #f8f9fa; clear:left" role="navigation"><!-- Spezial:Diff/124689226 --><div><span style="font-weight:bold" lang="{{int:lang}}">{{int:toc}}</span> [[#A{{{1\|}}}\|A]] [[#B{{{1\|}}}\|B]] [[#C{{{1\|}}}\|C]] [[#D{{{1\|}}}\|D]] [[#E{{{1\|}}}\|E]] [[#F{{{1\|}}}\|F]] [[#G{{{1\|}}}\|G]] [[#H{{{1\|}}}\|H]] [[#I{{{1\|}}}\|I]] [[#J{{{1\|}}}\|J]] [[#K{{{1\|}}}\|K]] [[#L{{{1\|}}}\|L]] [[#M{{{1\|}}}\|M]] [[#N{{{1\|}}}\|N]] [[#O{{{1\|}}}\|O]] [[#P{{{1\|}}}\|P]] [[#Q{{{1\|}}}\|Q]] [[#R{{{1\|}}}\|R]] [[#S{{{1\|}}}\|S]] [[#T{{{1\|}}}\|T]] [[#U{{{1\|}}}\|U]] [[#V{{{1\|}}}\|V]] [[#W{{{1\|}}}\|W]] [[#X{{{1\|}}}\|X]] [[#Y{{{1\|}}}\|Y]] [[#Z{{{1\|}}}\|Z]] [[#Categories{{{1\|}}}\|Categories]] {{{2\|}}}</div></div></onlyinclude>

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Oluschinski — Fri, 09 Oct 2026 11:03:55 GMT

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Mixed-Mode Crack Propagation

Oluschinski — Tue, 29 Sep 2026 05:26:06 GMT

← Older revision		Revision as of 07:26, 29 September 2026
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	==Application example poly(methyl methacrylate) (PMMA)==		==Application example poly(methyl methacrylate) (PMMA)==

	The device in '''Fig. 1''' with a [[~~Compact Tension Shear (~~CTS) Specimen \| CTS (Compact Tension Shear) test specimen]] made of poly(methyl methacrylate) ([[Plastics – Symbols and Abbreviated Terms \| abbreviation]]: PMMA) subjected to external tension enables the realization of pure modes I and II as well as mixed-mode I/II conditions by varying the angle ''φ'' between the notch and the direction of loading in the range from 0° to 90°.		The device in '''Fig. 1''' with a [[CTS-Specimen\|CTS (Compact Tension Shear) test specimen]] made of poly(methyl methacrylate) ([[Plastics – Symbols and Abbreviated Terms\|abbreviation]]: PMMA) subjected to external tension enables the realization of pure modes I and II as well as mixed-mode I/II conditions by varying the angle ''φ'' between the notch and the direction of loading in the range from 0° to 90°.

	[[file:Mixed-Mode_1.jpg\|500px]]		[[file:Mixed-Mode_1.jpg\|500px]]
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	\|}		\|}

	The nearly linear-elastic material ~~behavior~~ typical for PMMA allows the use of the ~~LEBM~~ to determine the stress intensity factor Kc according to the equation		The nearly linear-elastic material behaviour typical for PMMA allows the use of the LEFM to determine the stress intensity factor ''K''<sub>c</sub> according to the equation

	{\|		{\|
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	\|width="20px"\|		\|width="20px"\|
	\|width="500px" \| <math> f \left(\frac {a} {W}\right) = \frac {\sqrt {2\,\text{tan}{\frac{\pi\,a}{2\,W}}}} {\text {cos} \frac {\pi\,a} {2\,W}} \; \left[0.752 + 2.02 \left(\frac {a} {W} \right) + 0.37 \left(1 - \text {sin} \frac {\pi\,a} {2\,W} \right)^3 \right] </math>		\|width="500px" \| <math> f \left(\frac {a} {W}\right) = \frac {\sqrt {2\,\text{tan}{\frac{\pi\,a}{2\,W}}}} {\text {cos} \frac {\pi\,a} {2\,W}} \; \left[0.752 + 2.02 \left(\frac {a} {W} \right) + 0.37 \left(1 - \text {sin} \frac {\pi\,a} {2\,W} \right)^3 \right] </math>
	\|~~(2)~~		\|
	\|}		\|}

	and the maximum load ''F''<sub>max</sub> by evaluating the force–displacement diagrams recorded during the test. Here it means: ''B'' and ''W'' – test specimen thickness and width, ''a'' – notch depth.		and the maximum load ''F''<sub>max</sub> by evaluating the force–displacement diagrams recorded during the test. Here it means: ''B'' and ''W'' – test specimen thickness and width, ''a'' – notch depth.

	By determining the Mode I and Mode II parts ''K''<sub>I</sub> and ''K''<sub>II</sub> of the [[Fracture Mechanics \| stress intensity factor]] according to		By determining the Mode I and Mode II parts ''K''<sub>I</sub> and ''K''<sub>II</sub> of the [[Fracture Mechanics\|stress intensity factor]] according to

	{\|		{\|
	\|-		\|-
	\|width="20px"\|		\|width="20px"\|
	\|width="500px" \| <math> K_{I} = K_{Ic} \cdot \text {cos}^2 \varphi </math>		\|width="500px" \| <math> K_{I} = K_{Ic} \cdot \text {cos}^2 \varphi </math> <br>and<br><math> K_{II} = K_{IIc} \cdot \text {sin}^2 \varphi </math>
	~~\|(3)~~		\|(2)
	\|}
	and
	{\|
	\|-
	~~\|width="20px"\|~~
	~~\|width="500px" \|~~ <math> K_{II} = K_{IIc} \cdot \text {sin}^2 \varphi </math>
	\|(4)
	\|}		\|}

	By means of the experimentally determined fracture toughness under pure Mode I or pure Mode II loading (''K''<sub>Ic</sub> and ''K''<sub>IIc</sub> ), a comparative value ''K''<sub>V</sub> of the stress intensity factor with		By means of the experimentally determined fracture toughness under pure Mode I or pure Mode II loading (''K''<sub>Ic</sub> and ''K''<sub>IIc</sub>), a comparative value ''K''<sub>V</sub> of the stress intensity factor with

	{\|		{\|
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	\|width="20px"\|		\|width="20px"\|
	\|width="500px" \| <math> K_{V} = \sqrt {{K_I}^2 + {K_II}^2} </math>		\|width="500px" \| <math> K_{V} = \sqrt {{K_I}^2 + {K_II}^2} </math>
	\|(5)		\|(3)
	\|}		\|}

	and compare it with the experimental data ''K''<sub>c</sub> of the stress intensity factor according to equation (1), as shown in '''Fig. 3'''. The good agreement between the experimentally determined ''K''<sub>c</sub> values and the ''K''<sub>V</sub> values according to equation (5) can be explained by the assumption of a normal stress fracture hypothesis. The initial crack propagation angle ''β'' and the loading angle ''φ'' are identical up to about ''φ'' = 60°, i.e. the crack propagates perpendicular to the external stress according to this hypothesis ('''Fig. 4''').		and compare it with the experimental data ''K''<sub>c</sub> of the stress intensity factor according to equation (1), as shown in '''Fig. 3'''. The good agreement between the experimentally determined ''K''<sub>c</sub> values and the ''K''<sub>V</sub> values according to equation (3) can be explained by the assumption of a normal stress fracture hypothesis. The initial crack propagation angle ''β'' and the loading angle ''φ'' are identical up to about ''φ'' = 60°, i.e. the crack propagates perpendicular to the external stress according to this hypothesis ('''Fig. 4''').

	[[file:Mixed-Mode_3.jpg\|500px]]		[[file:Mixed-Mode_3.jpg\|500px]]
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	\|width="20px"\|		\|width="20px"\|
	\|width="500px" \| <math> \beta = - \text {arcsin} \left( \frac {M-3 \cdot \sqrt {M^2 + 8}} {M^2 + 9} \right) \text {with} \; M = \frac {K_I} {K_{II}} - \frac {T \cdot \sqrt {\pi \, a}} {K_c} </math>		\|width="500px" \| <math> \beta = - \text {arcsin} \left( \frac {M-3 \cdot \sqrt {M^2 + 8}} {M^2 + 9} \right) \text {with} \; M = \frac {K_I} {K_{II}} - \frac {T \cdot \sqrt {\pi \, a}} {K_c} </math>
	\|(6)		\|(4)
	\|}		\|}

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	\|- valign="top"		\|- valign="top"
	\|width="50px"\|'''Fig. 4''':		\|width="50px"\|'''Fig. 4''':
	\|width="600px"\|Crack initiation angle  as a function of the loading angle ''φ''		\|width="600px"\|Crack initiation angle ''β'' as a function of the loading angle ''φ''
	\|}		\|}

	In comparison to the singular stress parts of the stress field in cracked solids, which can be quantified by the stress intensity factor, the T-stresses are non-singular stress parts of constant magnitude parallel to the crack, which for [[SENT-Specimen \| Single-Edge-Notched Tension (SENT) test specimens]] under mixed-mode loading according to		In comparison to the singular stress parts of the stress field in cracked solids, which can be quantified by the stress intensity factor, the ''T''-stresses are non-singular stress parts of constant magnitude parallel to the crack, which for [[SENT-Specimen\|Single-Edge-Notched Tension (SENT) test specimens]] under mixed-mode loading according to

	{\|		{\|
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	\|width="20px"\|		\|width="20px"\|
	\|width="500px" \| <math> T = \frac {F_{max}} {B \cdot (W-a)} \cdot (\text {cos}^2 \varphi - \text {sin}^2 \varphi) </math>		\|width="500px" \| <math> T = \frac {F_{max}} {B \cdot (W-a)} \cdot (\text {cos}^2 \varphi - \text {sin}^2 \varphi) </math>
	\|(7)		\|(5)
	\|}		\|}
	can be estimated.		can be estimated.

	This means that, compared to the conventional MTS criterion, they lead to a further reduction in the crack propagation angle  for  > 45° according to equation (4).		This means that, compared to the conventional MTS criterion, they lead to a further reduction in the crack propagation angle ''β'' for ''φ'' > 45° according to equation (4).

	The crack initiation angles  calculated according to the modified MTS criterion tend to agree with the experimentally determined values, with  increasing up to  = 60° and changing less for  > 60° ('''Fig. 4''').		The crack initiation angles ''β'' calculated according to the modified MTS criterion tend to agree with the experimentally determined values, with ''β'' increasing up to ''φ'' = 60° and changing less for ''φ'' > 60° ('''Fig. 4''').

	==Mixed-mode I/II stress of thermoplastics==		==Mixed-mode I/II stress of thermoplastics==

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Mixed-Mode Crack Propagation