13 High Strain Rate Tension Experiments Features …
199
interpretation features are considered in works (Mirone 2013; Mirone et al. 2016).
The appropriate correction of deformation diagram is required after the necking point
(Bridgman 1955).
To evaluate effective true stresses, a number of methods have been proposed by
(Alves and Jones 1999; Dietrich et al. 1970; Gromada et al. 2011; La Rosa et al. 2003;
Ling 1996; Malinin and Rzysko 1981; Mirone 2004; Zhang et al. 1999; Bridgman
1955; Davidenkov and Spiridonova 1946).
The strain threshold of the initiation of localization can be determined by the
following conditions:
dσ 0
dε
= 0 or
dσ
dε
=
σ
1 + ε
or
dσ
de
= σ
(13.1)
here σ, σ 0 are true and engineering stresses, respectively, e, ε are true (logarithmic)
and engineering strains, respectively.
The Bridgman’s assumption on uniformity of plastic strain in the neck section
was experimentally confirmed by Aronofsky (1951). The assumption on similarity
of longitudinal grid lines in the neck was confirmed by Davidenkov and Spiridonova
(1946) The stress components distribution in the neck section proposed by Bridgman
is in good agreement with Zhang’s numerical analysis results (Zhang and Li 1994).
The main complexity of Bridgman’s method (and similar approaches) is caused
by the necessity of precise determination of minimum radius of the neck section
and neck curvature. Another technique of deformation diagram correction, based
on universal (material independent) polynomial, was proposed by Mirone (2004).
The coefficients of the polynomial are derived by generalization of a large amount
of experimental data. Mirone has showed (Mirone 2004, 2007; Mirone and Corallo
2010) that the proposed procedure is material independent and allows the proper
determination of effective stress with account for strain localization. The effective
true stress after necking prediction by Mirone’s procedure exhibits an error of about
5% for quasi-static elasto-plasticity (Mirone 2013).
The high rate video registration was used in (Gilat et al. 2009; Kajberg and Wikman
2007; Li 2017; Noble 1997) to obtain the specimen minimum radius history.
In (Bazhenov et al. 2013; Ling 1996; Sasso et al. 2008; Markov 2018) numerical
simulation was used to reconstruct the true deformation diagram based on tensile
experimental data.
The procedure of true stress–strain calculation is considered in detail in the next
section.
199
interpretation features are considered in works (Mirone 2013; Mirone et al. 2016).
The appropriate correction of deformation diagram is required after the necking point
(Bridgman 1955).
To evaluate effective true stresses, a number of methods have been proposed by
(Alves and Jones 1999; Dietrich et al. 1970; Gromada et al. 2011; La Rosa et al. 2003;
Ling 1996; Malinin and Rzysko 1981; Mirone 2004; Zhang et al. 1999; Bridgman
1955; Davidenkov and Spiridonova 1946).
The strain threshold of the initiation of localization can be determined by the
following conditions:
dσ 0
dε
= 0 or
dσ
dε
=
σ
1 + ε
or
dσ
de
= σ
(13.1)
here σ, σ 0 are true and engineering stresses, respectively, e, ε are true (logarithmic)
and engineering strains, respectively.
The Bridgman’s assumption on uniformity of plastic strain in the neck section
was experimentally confirmed by Aronofsky (1951). The assumption on similarity
of longitudinal grid lines in the neck was confirmed by Davidenkov and Spiridonova
(1946) The stress components distribution in the neck section proposed by Bridgman
is in good agreement with Zhang’s numerical analysis results (Zhang and Li 1994).
The main complexity of Bridgman’s method (and similar approaches) is caused
by the necessity of precise determination of minimum radius of the neck section
and neck curvature. Another technique of deformation diagram correction, based
on universal (material independent) polynomial, was proposed by Mirone (2004).
The coefficients of the polynomial are derived by generalization of a large amount
of experimental data. Mirone has showed (Mirone 2004, 2007; Mirone and Corallo
2010) that the proposed procedure is material independent and allows the proper
determination of effective stress with account for strain localization. The effective
true stress after necking prediction by Mirone’s procedure exhibits an error of about
5% for quasi-static elasto-plasticity (Mirone 2013).
The high rate video registration was used in (Gilat et al. 2009; Kajberg and Wikman
2007; Li 2017; Noble 1997) to obtain the specimen minimum radius history.
In (Bazhenov et al. 2013; Ling 1996; Sasso et al. 2008; Markov 2018) numerical
simulation was used to reconstruct the true deformation diagram based on tensile
experimental data.
The procedure of true stress–strain calculation is considered in detail in the next
section.