## Rate dependent isotropic plasticity (General case)

For steel at temperatures from 700 to 1300 °С we adopt a rate dependent plasticity model using the constitutive functions proposed by Brown  for the effective plastic strain rate was adopted in :

 {Mm)

 £p = Aexp(-^^-) RT

 sinh(^—) s and for evolution of the internal variable:

 (5-39)

 s = {hc

 (1~)

 Sign( --)}£P s

 (5-40)

where the temperature dependent term in (5-39), A exp(-AG/RT), is the reference ( for a given temperature) strain rate, m is a rate sensitivity, the hyperbolic sine accounts for the contribution of stress to thermal activated slip, h() is the reference hardening parameter

and s’ is the saturation value of deformation resistance s:

exp(—)

 є A
 (5-41)

RT

 Note that A , h()

exponents m and 1 and dimensionless

activation volume c, generally, are temperature and microstructure dependent material properties.
{"ft_lang_label":"__label__en","ft_lang_prob":0.78362924,"math_prob":0.9813865,"size":903,"snap":"2019-35-2019-39","text_gpt3_token_len":241,"char_repetition_ratio":0.11902113,"word_repetition_ratio":0.0,"special_character_ratio":0.2868217,"punctuation_ratio":0.07643312,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.951644,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-17T12:42:39Z\",\"WARC-Record-ID\":\"<urn:uuid:d412ea42-58b9-450f-8134-0b678a16e14f>\",\"Content-Length\":\"24770\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b2e8ad39-8d5a-4f8d-ab22-144a8706cf5f>\",\"WARC-Concurrent-To\":\"<urn:uuid:0ca14662-49e7-4f83-bfef-786342820e4b>\",\"WARC-IP-Address\":\"87.118.114.218\",\"WARC-Target-URI\":\"http://proizvodim.com/rate-dependent-isotropic-plasticity-general-case.html\",\"WARC-Payload-Digest\":\"sha1:3MT3TYC6VDRRBZV2GB3JPVBSBMUDQEW7\",\"WARC-Block-Digest\":\"sha1:LDYLKRCQGIQEGTPJFFKDVPLF7A5LCPMV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027313259.30_warc_CC-MAIN-20190817123129-20190817145129-00485.warc.gz\"}"}