# Failure Theories Why do parts fail? What kind of stresses?

## Presentation on theme: "Failure Theories Why do parts fail? What kind of stresses?"— Presentation transcript:

Failure Theories Why do parts fail? What kind of stresses?
What else should be considered?

Consider a tensile test specimen under load
σ τ

Plane Stress

Maximum Shear Stress Theory or Tresca Yield Criterion
Yielding begins whenever the maximum shear stress in any element of a structural member or machine part becomes equal to the maximum shear stress in a tensile test specimen of the same material when that specimen begins to yield.

Maximum Distortion Energy Theory or von Mises – Hencky Theory
When materials are deformed they store energy internally. The energy, u, stored per unit volume when a material undergoes a uniaxial stress, σ, that causes a strain, ε, can be defined in general as follows: By using Hooke’s law for a part subjected to a plane stress state, it can be shown that the amount of energy, ud, required to deform the part is as follows: For a uniaxial tensile test, the energy required to yield or deform a test specimen made from the same material as the part is as follows: By equating the energies, an equation can be developed that shows the relationship between the plane stress state defined by σ1 and σ2 in the part with the yield strength of a test specimen made from the same material:

Maximum Distortion Energy Theory (continued)

Download ppt "Failure Theories Why do parts fail? What kind of stresses?"

Similar presentations
{"ft_lang_label":"__label__en","ft_lang_prob":0.8805049,"math_prob":0.8642842,"size":1369,"snap":"2020-34-2020-40","text_gpt3_token_len":303,"char_repetition_ratio":0.12087912,"word_repetition_ratio":0.04310345,"special_character_ratio":0.20087655,"punctuation_ratio":0.08880309,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9564514,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-19T08:11:13Z\",\"WARC-Record-ID\":\"<urn:uuid:617ba686-3e5a-4332-a959-9297fc3f1373>\",\"Content-Length\":\"157895\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1398ac85-3bbc-4917-8dd2-02a3543e4d81>\",\"WARC-Concurrent-To\":\"<urn:uuid:50d8e278-03d6-414f-b5d4-7f86d12060c1>\",\"WARC-IP-Address\":\"88.99.70.210\",\"WARC-Target-URI\":\"https://slideplayer.com/slide/4978078/\",\"WARC-Payload-Digest\":\"sha1:E6DT2PNKPBNZT43LBUK3HJZYYB3R4CVU\",\"WARC-Block-Digest\":\"sha1:GRBRZ3IKY3C2CZ23D6OQLAXVTTJTKGG3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400191160.14_warc_CC-MAIN-20200919075646-20200919105646-00444.warc.gz\"}"}