Yield Criteria

SOLID MECHANICS II BMCS 3333

Yield Criteria -Failure Analysis -SOLID MECHANICS IIBMCS 3333Universiti Teknikal Malaysia Melaka (UTeM)

Nadlene Razali

Failures overviewThere are various type mode of failures :

Fracture mechanic Fatigue Structure instability (buckling)

IntroductionIntroduction

Few example of failures: Structural failure

IntroductionStructural failure

Tacoma Narrows Bridge collapsedIntroduction

Structural support for spherical storage tank collapseIntroduction

Coal stacking belt failure, in Pennsylvania.Introduction

Hydrogen embrittlement fracture surface of a bolt showing multiple initiation sites. The fastener was one of eight body bolts in a high pressure pump that failed after years in atmospheric service.Introduction

A natural gas pipeline in Venezuela ruptured next to a major highway in September, 1993. The subsequent gas jet ignition resulted in an inferno that killed at least 50 people. Introduction

The Heverill Fire Department aerial ladder failure. Structural failure of a ladder is not at all an uncommon event. Failure can result from poor design, use of inferior material, fabrication methods, or from a phenomenon called fatigue. Introduction

During a violent storm on the evening of 28 December 1879, the centre section of the bridge, known as the "High Girders", collapsed, taking with it a train that was running on its single track. More than 75 lives were lost. Tay Bridge disaster (1879), in Scotland.Introduction

SS AMERICA - Queen of the American Merchant Marine. Designed and constructed at the zenith of transatlantic passenger ship service in the late 1930s.Introduction

Due to hurricane-strength winds and mountainous waves continued to pound the hapless. Over 55 years since first being riveted together - suffered a total fracture (1994); the result of metal fatigue. IntroductionLoading Types:

Static load Dynamic load Thermal Cyclic LoadIntroduction

Static or static load : sometimes a load is assumed to be static when it is known that some variation is to be expected.

Introduction

Mode of FailureIntroductionDuctile MaterialBrittle MaterialFailure Analysis

Yield Criteria Failure AnalysisDuctile MaterialBrittle MaterialFail after yield point which are cause by slippingSuddenly fracture with no apparent yieldingMaximum Shear Stress Theory Tresca yield criterionMaximum Distortion Energy Theory von-MisesMaximum Normal Stress Theory - RankineMohrs Failure CriterionDuctile material gives large tensile strain before fracture. Failure is specified by the initiation of yielding.Ductile failure can be defined when slipping occurs between the crystals that compose material. This slipping is due to the shear stress.The edges of the planes of slipping appear at the surface of the strip referred to as Luders lines.

Example of ductile material: steels and aluminum

Theories of Failure for Ductile MaterialLuders lines - 450 to the strip axisYield Criteria for Ductile Materials Under Plane Stress

Failure of a machine component subjected to uniaxial stress is directly predicted from an equivalent tensile test.Failure of a machine component subjected to plane stress cannot be directly predicted from the uniaxial state of stress in a tensile test specimen.It is convenient to determine the principal stresses and to base the failure criteria on the corresponding biaxial stress state.Failure criteria are based on the mechanism of failure. Allows comparison of the failure conditions for a uniaxial stress test and biaxial component loading.Yield Criteria for Ductile Materials Under Plane Stress

Maximum shearing stress criteria:Structural component is safe as long as the maximum shearing stress is less than the maximum shearing stress in a tensile test specimen at yield, i.e.,

For sa and sb with the same sign,

For sa and sb with opposite signs,

Tresca Yield CriterionMaximum-Distortion-Energy Theory

Energy per unit volume of material is called the strain-energy density.Material subjected to a uniaxial stress , the strain-energy density is written as,

Yield Criteria for Ductile Materials Under Plane StressFor linear-elastic behavior, applying Hookes law into above equation:

Maximum-distortion-energy theory is defined as the yielding of a ductile material occurs when the distortion energy per unit volume of the material equals or exceeds the distortion energy per unit volume of the same material when subjected to yielding in a simple tension test.

Yield Criteria for Ductile Materials Under Plane StressDistortion energy per unit volume in anisotropic material under plane stress,

For uniaxial tension test, 1 = Y, 2 = 3 = 0. Therefore,

Yield Criteria for Ductile Materials Under Plane StressSince maximum-distortion energy theory requires ud = (ud)Y , then for the case of plane or biaxial stress, we have:

Yield Criteria for Ductile Materials Under Plane Stress

Maximum distortion energy criteria (von Mises):Structural component is safe as long as the distortion energy per unit volume is less than that occurring in a tensile test specimen at yield.

WhereYield Criteria for Ductile Materials Under Plane Stress

Comparison between maximum-shear stress and maximum-distortion energy criteria.Actual torsion test result show tY/sY range from 0.55 to 0.60. Thus, the maximum-distortion-energy theory appears more accurate.

Yield Criteria for Ductile Materials Under Plane Stress

Maximum normal stress criteria:Structural component is safe as long as the maximum normal stress is less than the ultimate strength of a tensile test specimen.

Brittle materials fail suddenly through rupture or fracture in a tensile test. The failure condition is characterized by the ultimate strength sU.

Yield Criteria for Brittle Materials Under Plane Stress

Be aware some F.S. based on ultimate tensile stressThe factor reduces the failure stress level to a value called working stress which, under foreseen operating condition, the material in component part of a design will have to withstand.Factor of safety

It is needed due to: Mathematical models only approximation. Material property vary from batch to batch. Type of loading produce unknown stresses. Residual stresses from manufacturing processes. Effect of environment, heat, ageing, corrosion etc.General guidelines of F.S.1.2 1.5:Reliable materials under controllable condition.1.5 2.0:Well known materials under reasonably constant environmental conditions and loads and stresses easily determined.2.0 2.5:Average material. Also known Service Factors.2.0 4.0:For less tried material.5.0 7.0:Impact loading, to prevent failure.Factor of safety

Example:

For the state of stress shown, determine the maximum shearing stress when:a) y = 20 MPab) y = 140 MPaYield Criteria Failure Analysis

Solution:

Yield Criteria Failure Analysis

Yield Criteria Failure AnalysisIf the material yields in uniaxial simple tension at a stress y = 210 MPa, investigate whether it will yield according to the maximum shear stress criteria (tresca criteria) for both cases (a) and (b)?Tresca criteria,Yielding when

Thus,For case (a), max = 100 MPa < 210 /2 . Not yielding.For case (b), max = 110 MPa > 210 /2 . Yielding occurs.Example Yield Criteria Failure AnalysisExample:

A steel pipe has inner diameter of 60 mm and outer diameter of 80 mm. It is subjected to a torsional moment of 8 kNm and a bending moment of 3.5 kNm.By using maximum-distortion-energy theory, determine whether the steel pipe will fail or not? (Given that Y = 250 MPa).Yield Criteria Failure AnalysisSolution: Torsional and bending moments are uniform throughout the pipes length.At arbitrary section a-a, loadings produce the stress distributions shown.

Yield Criteria Failure AnalysisBy inspection, points A and B subjected to same state of critical stress.


= 127.1

Yield Criteria Failure AnalysisUsing maximum distortion energy criterion (von mises),

= 226 MPa < ySince criterion is met, material within the pipe will not yield (fail) according to the maximum-distortion-energy theory._________________________________________________________________________________________________________________Kamarul Ariffin, FKM, UTeM BMCS 2333- 2008Yield Criteria Failure AnalysisExample:

The state of plane stress shown occurs in a machine component made of a steel with y = 210. Using the maximum distortion energy criterion (Von mises criterion) determine whether yield occurs when:xy = 42 MPaxy = 84 MPaxy = 98 MPaIf yields does not occur, determine the corresponding factor of safety.Yield Criteria Failure AnalysisSolution:




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Yield Criteria