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	* [[Fracture Mechanics\|Fracture mechanics]]		* [[Fracture Mechanics\|Fracture mechanics]]
	* [[Deformation]]		* [[Deformation]]
	* [[ICIT – Experimental Conditions\|ICIT – ~~experimental~~ conditions]]		* [[ICIT – Experimental Conditions\|ICIT – Experimental conditions]]
	* [[Instrumented Charpy Impact Test\|Instrumented Charpy impact test]]		* [[Instrumented Charpy Impact Test\|Instrumented Charpy impact test]]
	* [[Viscoelastic Material Behaviour\|Viscoelastic material behaviour]]		* [[Viscoelastic Material Behaviour\|Viscoelastic material behaviour]]

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{{Language_sel|LANG=ger|ARTIKEL=IKBV Nichtlineares Werkstoffverhalten}}
{{PSM_Infobox}}
ICIT – Nonlinear material behaviour
__FORCETOC__

==Determination of impact load FGY and deflection fGY for elastic–plastic material behaviour==

The dominant evaluation method problem of the [[Instrumented Charpy Impact Test|instrumented Charpy impact test]] in determining fracture mechanical material parameters from impact load (F)–deflection (f) diagrams with nonlinear material behaviour lies in the determination of the force ''F''GY at the transition from elastic to elastic–plastic material behaviour and the associated deflection ''f''GY [1, 2].

==Typical impact load‒deflection diagrams for polypropylene (PP)==

The problem of determining the [[Measured Variable|measured variables]] from the F–f diagram will be explained using the example of investigations into the dependence on the ''a''/''W'' ratio for a polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) material at room temperature.

[[file:ICIT - Non-linear Material Behaviour 1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Typical impact load (F)–deflection (f) diagrams for polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) at different ''a''/''W'' ratios
|}

'''Figure 1''' shows typical F–f diagrams for the various ''a''/''W'' ratios 0.1, 0.3, 0.45, and 0.7 (see also: ICIT – [[ICIT – Types of Impact Load–Deflection Diagrams|types of impact load–deflection diagrams]]).

The F–f diagrams shown indicate that

# the relationship between impact load and specimen deflection becomes increasingly nonlinear as the ''a''/''W'' ratio increases
# the maximum impact load ''F''max decreases as the ''a''/''W'' ratio increases, and
# the amplitude of the [[Inertial Load|inertial load]] ''F''1 remains approximately constant.

For ''a''/''W'' > 0.7, the forces ''F''max and ''F''GY become so small in comparison to the superimposed oscillation that the condition ''F''max > ''F''1 (see also: [[ICIT – Experimental Conditions|ICIT – experimental conditions]]) can no longer be fulfilled and it is not possible to determine them meaningfully in the recording diagram.

==Results for selected plastics==

Analogous results were also obtained in [1] for a post-chlorinated PVC material ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PVC-C) [3, 4], two polyamide ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PA) materials [4, 5], a high-density polyethylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PE-HD) [5], on PE-HD filled with cotton (BW) and on PE-HD filled with hard paper (HP) [6].

'''Figure 2''' shows the decrease in maximum impact load ''F''max with increasing ''a''/''W'' ratio, i.e., smaller residual cross-section for these materials.

[[file:ICIT - Non-linear Material Behaviour 2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Dependence of the maximum impact load ''F''max on the ''a''/''W'' ratio for selected [[Plastics|plastics]]
|}

In order to generate suitable F–f diagrams for the evaluation, the demand for the use of a low ''a''/''W'' ratio is derived from the results presented, whereby the evaluability of the diagrams must be ensured by complying with the control condition explained under “[[ICIT – Experimental Conditions|ICIT – experimental conditions]]” with regard to the [[Inertial Load|inertial load]], the fracture time and the energy consumption.

This requirement is in contrast to the requirements set out in various standards, e.g. in [7], according to which the ''a''/''W'' ratio should be 0.35 ≤ ''a''/''W'' ≤ 0.55 for application according to the concept of linear-elastic fracture mechanics (LEBM) (see also: [[Fracture Mechanics|fracture mechanics]]) or the [[Equivalent Energy Concept – Basics|equivalent energy concept]]. The loads ''F''max and ''F''GY determined from the F–f diagrams decrease with the decrease in the residual cross-section ''B''(''W''-''a'') for the materials investigated, as shown in '''Fig. 3'''.

[[file:ICIT - Non-linear Material Behaviour_3a.jpg]]

[[file:ICIT - Non-linear Material Behaviour_3b.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Dependence of the loads Fmax, FGY (a) and the corresponding deflections fmax, fGY (b) for polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP) on the ''a''/''W'' ratio
|}

==Evaluation of the non-linearity of material behaviour==

Information about the non-linearity is provided by the ratio ''F''max/''F''GY, which is plotted in the partial image in '''Fig. 3''' as a function of the ''a''/''W'' ratio. For ''F''max/''F''GY = 1, [[Fracture Mechanics#Linear-elastic fracture mechanics|linear-elastic fracture mechanics (LEFM)]] must be applied and for ''F''max/''F''GY > 1, [[Fracture Mechanics#Elastic–plastic_fracture_mechanics_(EPFM)|elastic–plastic fracture mechanics (EPFM)]] must be applied. Not unproblematic in its interpretation is the course of the deflection with increasing ''a''/''W'' ratio, which, in addition to the problem of the bending of the notched test [[Specimen|specimen]] with large deflections and the change in the notch factor αK with the [[Notch Geometry|notch geometry]], also contains the additional possible effect of the “pulling through” of the test [[Specimen|specimens]] through the abutments, at least for large [[Support Distance|support distance]] [1]. If the ratio of the deflections ''f''max/''f''GY is taken as a measure of the non-linearity, it can be seen that this increase is a sensitive indicator of the non-linearity and allows a statement to be made about the fracture mechanics concept to be applied.

Assuming [1, 8] that the experimentally measured specimen deflection ''f''max is calculated of the unnotched part ''f''B and the part ''f''K caused by the deformation in the area of the notch according to

{|
|-
|width="20px"|
|width="500px" | <math>f_{max} = f_{k} + f_{B} </math>
|(1)
|}

whereby the bending component is determined via the relationship

{|
|-
|width="20px"|
|width="500px" | <math>f_{B} = \frac{F_{max} \cdot s^{3}}{4 BW^{3} E} </math>
|(2)
|}

with ''E'' = [[Elastic Modulus|modulus of elasticity]] in the [[Bend Test|bending test]], the relationship shown in '''Fig. 3''' can be interpreted (see also: [[Extended CTOD Concept|extended CTOD concept]]).

'''Figure 4''' shows the individual parts according to equation (1) as a function of the ''a''/''W'' ratio using the example of a polypropylene material ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP).

[[file:ICIT - Non-linear Material Behaviour_4.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px" |Deflection parts fmax, fK and fB at the beginning of unstable crack growth for polypropylene ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP)
|}

'''Figure 4''' shows that the bending component decreases with increasing ''a''/''W'' ratio, 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 part ''f''K dominates.

In [1] it is shown for materials with higher elastic proportions of the total deformation, such as selected PA materials and PVC-C, that the bending proportion is considerably higher in this case.

==See also==

* [[Fracture Mechanics|Fracture mechanics]]
* [[Deformation]]
* [[ICIT – Experimental Conditions|ICIT – experimental conditions]]
* [[Instrumented Charpy Impact Test|Instrumented Charpy impact test]]
* [[Viscoelastic Material Behaviour|Viscoelastic material behaviour]]

'''References'''

{|
|-valign="top"
|[1]
|[[Grellmann, Wolfgang|Grellmann, W.]]: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), [https://de.wikipedia.org/wiki/Technische_Hochschule_Leuna-Merseburg Technischen Hochschule Merseburg], Wiss. Zeitschrift TH Merseburg 28 (1986), H. 6, pp. 787–788 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Inhaltsverzeichnis.pdf Content], [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Kurzfassung.pdf Summary])
|-valign="top"
|[2]
|Server, W. L.: Impact Three-point Bend Testing for Notched and Precracked Specimens. Journal of Testing and Evaluations JTEVA, 6 (1978) 1, 29–34
|-valign="top"
|[3]
|Hoffmann, H., [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.]: Zur Bestimmung der dynamischen Bruchzähigkeit von Polymerwerkstoffen im instrumentierten Kerbschlagbiegeversuch. Plaste und Kautschuk 30 (1983) Publ. Nr. 14 H. 6, 324‒330 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Publ_14_Plaste_und_Kautschuk_30_1983__H_6_S_324-330.pdf Download as pdf])
|-valign="top"
|[4]
|Hoffmann, H., [https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.], Zilvar, V. Sommer, J. P., Michel, B.: Anwendung verschiedener J-Integral-Näherungsverfahren zur Beschreibung der Zähigkeitseigenschaften von Polymerwerkstoffen. Wiss. Zeitschrift der THLM 28 (1986) H 1, 58‒67
|-valign="top"
|[5]
|Eve, S.: Untersuchungen zum Einfluss der Kerbtiefe und der Hammergeschwindigkeit auf die dynamische Bruchzähigkeit mit Hilfe des instrumentierten Kerbschlagbiegeversuches. Ingenieurbeleg TH Leuna-Merseburg, 1983 (siehe [[AMK-Büchersammlung|AMK-Library]] unter B 3-15)
|-valign="top"
|[6]
|[[Seidler, Sabine|Seidler, S.]]: Kerbschlagbiegeverhalten von gefüllten und verstärkten Polymerwerkstoffen. Ingenieurbeleg, TH Leuna-Merseburg 1983 (see [[AMK-Büchersammlung|AMK-Library]] under B 2-14)
|-valign="top"
|[7]
|ASTM E 399 (2024): Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards; DOI: 10.1520/E0399-24
|-valign="top"
|[8]
|Srawley, J. E.: On the Relation of JI to Work Done per Unit Incracked Area: 'Total', or Component "Due to Crack". Intern. Journal of Fracture Mechanics 12 (1976) 470‒474; https://link.springer.com/article/10.1007/BF00032843#citeas
|}

[[category:Fracture Mechanics]]
[[category:Instrumented Impact Test]]

ICIT – Nonlinear Material Behaviour - Revision history

Oluschinski at 05:23, 15 December 2025