the hypothesis of failure summary pdf

The Hypotheses Of Failure

By o. henry.

Return to the O. Henry library , or . . . Read the next short story; The Indian Summer Of Dry Valley Johnson

The Hypotheses of Failure (Henry)

A lawyer named Phineas C. Gooch specialized in handling divorce cases. One day, a confident and well-dressed man visited Gooch's office, seeking advice on a hypothetical case involving a woman who had left her husband for another man.

The man claimed that the woman's husband, Thomas R. Billings, was incompatible with her, and that the other man, Henry K. Jessup, was a better match. The visitor offered to pay Gooch $500 to secure a divorce for the woman.

Shortly after, a woman entered Gooch's office, presenting a similar hypothetical case. She revealed herself to be Mrs. Billings and asked Gooch to help her obtain a divorce. Gooch then met with a third client, who claimed to be Thomas R. Billings.

This man begged Gooch to convince his wife to return home and offered to pay $1,000 for his services.

‘A divorce!’ exclaimed the client, feelingly—almost tearfully. ‘No, no—not that. I have read, Mr. Gooch, of many instances where your sympathy and kindly interest led you to act as a mediator between estranged husband and wife, and brought them together again. Let us drop the hypothetical case—I need conceal no longer that it is I who am the sufferer in this sad affair—the names you shall have—Thomas R. Billings and wife—and Henry K. Jessup, the man with whom she is infatuated.’

Gooch realized that all three clients were connected and attempted to bring them together to resolve the situation. However, the third client panicked upon learning that his wife was in the building and fled, leaving behind a satchel containing items belonging to Henry K. Jessup. Gooch discovered that the third client was actually Jessup in disguise, and decided not to take on the case.

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Henry, O., 1862-1910. The Hypothesis of Failure , prose (fiction) , January 1904; ( https://texashistory.unt.edu/ark:/67531/metapth139386/m1/2/ : accessed April 16, 2024 ), University of North Texas Libraries, The Portal to Texas History, texashistory.unt.edu ; .

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O.Henry The Hypotheses of Failure Summary

Lawyer Gooch was a dedicated professional who compared his office to the bottom of a ship, with separate compartments to handle conflicting clients. He specialized in marital disputes, often reuniting couples and receiving substantial fees for his services.

A confident visitor approached him seeking a divorce for a woman involved with another man, offering a generous sum for his assistance. The visitor emphasized the incompatibility between the woman and her husband, justifying the need for a divorce.

Despite the hypothetical scenario presented, the visitor was eager to proceed with real business, offering a significant payment for Lawyer Gooch’s services. Just as they were about to discuss further, a new client arrived, interrupting their conversation.

Lawyer Gooch was approached by two clients with marital issues. The first, a wealthy lady seeking a divorce, presented a hypothetical case involving a mismatched marriage and a new love interest.

The second client, a distressed man, revealed himself as the husband in the hypothetical case and sought Lawyer Gooch’s help in reuniting with his wife. The lawyer, known for mediating between estranged couples, agreed to take on the case and persuade Mrs. Billings to return home.

The distressed husband offered a substantial sum of money as a reward for Lawyer Gooch’s assistance. The lawyer, though initially hesitant due to the difficulty of the task, ultimately agreed to help reunite the couple.

Lawyer Gooch thrived on intricate cases and relished the power he held over the fate of his clients. He attempted to negotiate fees with his clients, but failed to reach an agreement with the first one due to financial constraints.

The second client, Mr. Billings, was shocked to find his wife in the room and reacted violently, throwing his satchel at Lawyer Gooch before fleeing. The satchel contained items belonging to Henry K. Jessup, revealing Mr. Billings’ true identity. Lawyer Gooch, unfazed by the chaos, decided to walk away from the situation and informed his office boy to convey to the lady waiting that there would be no resolution.

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The Failure Analysis Process—An Overview

• Technical Article---Peer-Reviewed
• Published: 11 February 2022
• Volume 22 , pages 42–57, ( 2022 )

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• Debbie Aliya 1  

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Failure analysis is a process that is performed in order to determine the causes or factors that have led to an undesired loss of functionality. This article is intended to demonstrate proper approaches to failure analysis work. The goal of the proper approach is to allow the most useful and relevant information to be obtained. The discussion covers the principles and approaches in failure analysis work, objectives and scopes of failure analysis, the planning stages for failure analysis, the preparation of a protocol for a failure analysis, practices used by failure analysts, and procedures of failure analysis.

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© 2021 ASM International. This article is reprinted with permission from Failure Analysis and Prevention , Vol 11, 2021 ed., ASM Handbook , Brett A. Miller, Roch J. Shipley, Ronald J. Parrington, and Daniel P. Dennies, editors, ASM International, 2021, p 27–35, https://doi.org/10.31399/asm.hb.v11.a0006754 .

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Aliya, D. The Failure Analysis Process—An Overview. J Fail. Anal. and Preven. 22 , 42–57 (2022). https://doi.org/10.1007/s11668-021-01328-y

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ME 323 – Mechanics of Materials

Lecture 40-41: Failure analysis (static failure theories) Joshua Pribe Fall 2019 Lecture Book: Ch. 15 Motivation

• We have spent the last few classes finding the state of stress at various points in a body due to combined loading • We have seen various combinations of normal stresses and shear stresses

• Mohr’s circle gives us a way to compare different states of stress • For any state of stress, we can identify three important parameters: the two in-plane principal stresses and the absolute maximum shear stress

• Now: how can we use this information to predict whether a point in a body will fail? • First, we need to define what “failure” means…this depends on the type of material!

2 Failure theories overview

• Use the results of “simple” tests to formulate hypotheses • Usual hypothesis: the mechanism that causes failure in a tensile test is the same mechanism that causes failure in more complex stress states • We have different failure theories for brittle and ductile materials • “All models are wrong, but some are useful”

3 The tensile test Lecture Book: Ch. 15, pg. 2

Free-body diagram Mohr’s circle at any point on any cross section

What is the maximum normal stress? On which plane does this stress exist?

What is the maximum shear stress? On which planes does this stress exist?

4 Brittle failure: Maximum normal stress theory

Hypothesis: A brittle material fractures when the maximum principal stress equals or exceeds the ultimate normal stress when fracture occurs in a tensile test Define this “ultimate normal stress” as the ultimate strength Assumption: the ultimate strength in tension and compression is the same

Lecture Book: Ch. 15, pg. 11 5 Brittle failure: Maximum normal stress theory

We can visualize the failure boundary in principal stress space

Failure criteria Factor of safety

Lecture Book: Ch. 15, pg. 11 6 Brittle failure: Mohr’s theory

Modification to maximum normal stress theory based on the observation that many materials

are stronger in compression than they are in tension, i.e.  UT  UC , and the maximum normal stress theory is non-conservative when the principal stresses have different signs

7 Lecture Book: Ch. 15, pg. 12 Brittle failure: Mohr’s theory

For a general state of plane stress , there are three possible situations Lecture Book: Ch. 15, pg. 6

Case 1: pp120 Case 2: pp120 Case 3: 0 pp12

8 Lecture Book: Ch. 15, pg. 12 Brittle failure: Mohr’s theory

We can visualize the failure boundary in principal stress space Failure criteria Factor of safety

Case 1: pp120

Case 2: pp120  pp12−1 UT UC

Case 3: 0 pp12

p2 − UC 9 Lecture Book: Ch. 15, pg. 12

Brittle failure: Summary

Maximum normal stress theory Mohr’s failure theory Failure criterion Failure criteria (3 possible cases based on the signs of the principal stresses

p1 p2 0:  p1  UT 0:  pp1   2  pU2 − C pU1  or pU2 −  Factor of safety  0: p1 − p2 1 pp12    UT UC FS = U or FS = U  p1  p2 Factor of safety     0: FS = UT 0:  FS = UC (whichever is smaller is the real p1 p2 pp1 2  p1  p2 factor of safety) 1  0: FS = = UT UC p12p   −   pp12− p12 UC p UT UT UC

10 Example 15.7

The state of stress shown exists at a location in a component made of a brittle material with UC = 850 MaP and  UT = 17 0 Ma P . According to Mohr’s theory, has the material failed?

Ductile failure: Maximum shear stress theory • On the microscale, permanent (plastic) deformation occurs by “slip”

• Failure in a tensile test of a ductile material often looks very similar

12 Ductile failure: Maximum shear stress theory

Hypothesis: for any stress state, yielding of a ductile material occurs when the absolute maximum shear stress equals or exceeds the maximum shear stress when yielding occurs in a tensile test Lecture Book: Ch. 15, pg. 5

13 Lecture Book: Ch. 15, pg. 5 Ductile failure: Maximum shear stress theory

For a general state of plane stress, there are three possible situations Lecture Book: Ch. 15, pg. 6

Ductile failure: Maximum shear stress theory

We can visualize the failure boundary in principal stress space Lecture Book: Ch. 15, pg. 7 Failure criteria Factor of safety

Case 2: pp120

p12−  p  Y

15 Ductile failure: Maximum distortional energy theory

von Mises proposed a different hypothesis: yielding occurs when the distortion energy density equals or exceeds the distortion energy density when yielding occurs in a tensile test

Evidence: a material subjected to purely hydrostatic stress (  p 1 ==  p 2  p 3 ) never yields Total elastic strain energy density = change of volume + distortion (change of shape) 1 22 1 1 u =+ − 2   22 p1 p 2 p 1 p 2 uv=+( p12 p ) ud=( p1 −  p 1  p 2 +  p 2 ) 2E 2G 6G

For yielding in the tensile test So, our failure criterion for any plane stress state is

1 2 1 221 2 ud, yield =  Y (p1−+  p 1  p 2  p2 ) = Y 6G 6G 6G

Lecture Book: Ch. 15, pg. 8 16 Ductile failure: Maximum distortional energy theory

In principal stress space, the maximum distortional energy failure boundary is an ellipse

−   max = 1 3  Y abs 22

Failure criterion Factor of safety

 M  Y 22 where M=  p1 −  p 1  p 2 +  p 2 17 Ductile failure: Summary

Maximum shear stress theory Maximum distortional energy (von Mises) theory  Failure criterion:  abs  Y Failure criterion (based on the von Mises stress): max 2 22 abs M=  p1−+  p 1  p 2  p 2  Y 3 possible cases for  max based on signs of principal stresses

p1  p2  0:  p1  Y 0:pp12pY2 

Y  p12 0:− p  pp12 Y Factor of safety: FS =  M

Or, if you re-order the principal stresses so  1   2  3 , −   max = 1 3  Y is the failure criterion for all cases abs 22  Factor of safety: YY FS ==abs 2max 13− 

18 Example 15.1

The state of stress shown is in a component made of a ductile material with a yield strength of  Y = 250 MPa . Does the maximum shear stress theory predict failure for the material? Does the maximum distortion energy predict failure for the material?

Revisit Example 14.12

Wind blowing on a sign produces a resultant force P in the –y direction at the point shown. The support pole weighs WP and the sign weighs Ws. The pole is a pipe with outer and inner diameters do and di, respectively.

What are the factors of safety for points a and b according to the maximum distortion energy theory if the pole is made from an aluminum alloy with a yield strength of 20 ksi?

Bonus example

Determine the principal stresses and the maximum shear stress at point A (i.e., the point on top of the wrench handle). The diameter of the circular cross section is 12.5 mm.

If the wrench is made of a ductile material with a yield strength of 300 MPa, what value of the force will cause yielding at point A according to the maximum shear stress theory? How about the maximum distortion energy theory?

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