FACTOR OF SAFETY AND INDICATORS OF FAILURE

INDICATORS OF FAILURE

Failure of a machine part in static loading may be indicated by one of three events:

1)Ductile material yielding because induced stress has reached yield strength

2)Brittle material fracture because induced stress has reached ultimate strength

3)Excessive deflection of the part that causes loss of function, including slender column where the deflection causes elastic instability and buckling

BRITTLE VERSUS DUCTILE MATERIAL

A rough guide employs percent elongation at fracture obtained from the tensile test of the material

1)Ductile materials have Percent Elongation > 5%

2)Brittle materials have Percent Elongation<5%

FACTOR OF SAFETY AND ASSESSMENT OF ADEQUACY

Design considerations for a machine part are factors or variables that are expected to influence the part’s performance of its intended function. Such factors include:

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1)Ability to perform function

2)Strength/ stress

3)Deflection/rigidity

4)Wear/resistance to indentation

5)Corrosion resistance

6)Manufacturability

7)Reliability

8)Maintainability e.t.c

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The design seeks to ensure that the factors or considerations are enough[1], (adequate but not wasteful).

Assessing the part for adequacy with respect to a particular consideration consists of determining the indicator value required, and the margin by which that indicator value is exceeded.

ADEQUACY ASSESSMENT OFSTRENGTH VERSUS STRESS

1)For a part subject to external load, various indicators of strength which may be used are tensile strength, yield strength, fatigue strength etc. The indicator of strength to be applied will depend on the material from which the part is made, and the type of load (static or variable)

2)To test for adequacy, a stress identified as relevant, because it is the one expected to cause failure, and this stress may be tensile, shear, principal, von-Mises, etc

3)A particular location of the part is identified as the location where failure is expected to occur, and the pair of strength and stress selected is compared at this location.

4)Adequacy is the margin by which the strength exceeds the stress, so that failure is avoided

5)Adequacy therefore depends on how accurately the strength and stress are known,

6)Adequacy also depends on what margin between strength and stress is enough

7)The adequacy of the part with respect to strength can therefore be assessed by comparing the strength of the part to the stress induced at the chosen location of the part

8)When the strength and stress are compared by dividing the strength by the stress, the adequacy assessment is referred to as the factor of safety, or design factor.

9)When design starts with a material of known strength, the next step is to choose geometry and dimension of the part that is able to carry the object load.

10)A factor of safety therefore identifies an allowable stress, or design stress that is used to determine required dimension for the part.

11)The allowable stress is the strength divided by the factor of safety.

12)Where the design is complete, the actual factor of safety is determined by comparing the strength of the part, with the stress induced when the part of known dimension is subject to the object load.

FACTOR OF SAFETY FOR OTHER MEASURES OF LOSS OF FUNCTION

1)The factor of safety can be generalized to be applied to other indicators that signify loss of function for the part, such as load and deflection.

2)For example, a slender column subject to compression will fail by buckling, and the loss of function is therefore signified by the buckling load, rather than the compressive strength. The buckling load can therefore be used as the loss of function load, to be compared with expected load to obtain a factor of safety for the column.

3)Similarly, in the case of a member where failure is indicated by a certain value of deflection that would cause loss of function, then that loss of function deflection can be used for comparison with the expected deflection, and a factor of safety obtained to assess adequacy.

4)What if the loss of function occurs as a result surface failure in fatigue caused by contact stresses?

5)The consequence of failure, in this case, is seen as wear of the surface after several load applications.

6)A limit for the wear of the part can then be specified in terms of a life (number of load applications) before a certain level of wear occurs.

7)A load that will give the desired life can then be chosen as the safe load, since a greater load will reduce the life.

8)Loss of function from wear is a gradual occurrence and the specification of life therefore answers the question of what is the margin between loss of function load and the operating load.

SELECTING THE FACTOR OF SAFETY

Variables that influence the selection of the factor of safety are:

1)Material property used as the indicator of loss of function such as strength, loss of function load, loss of function deflection etc, and its variation or uncertainty

2)Expected variation or uncertainty in the final dimensions of the part, which cannot be controlled by design, because it is in the manufacturing process

3)Assumptions employed in the design analysis as a means of predicting stress and deflection from the load applied

CHOOSING THE MAGNITUDE OF THE FACTOR OF SAFETY

One of the major factors influencing the magnitude of the factor of safety to be employed in design is the expected consequence of failure. Consequences of failure can be classified in categories such as:

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1)Inconvenience

2)Loss of time

3)Financial loss

4)Loss of life

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CODES OF PRACTICE AND REGULATIONS

When product failure is likely to cause loss of life, codes of practice are developed as part of national and international standards to prescribe the factor of safety that will prevent failure and therefore loss of life.

Examples of such codes of practice and standards are available for design of pressure vessels and boilers

In such standards, the material to be used, the material properties, and the allowable stresses are specified, and hence the factor of safety is specified.

CHOOSING THE FACTOR OF SAFETY FOR OTHER MACHINE PARTS

For other machine parts where the designer is free to choose the factor of safety, this is done by considering the material concerned and the mode of failure expected.

GUIDELINES[2] FOR CAST IRON SUBJECT TO STATIC LOADING

1)The indicator of failure is ultimate tensile or compressive strength

2)Failure is expected to occur when the tensile or compressive stress reaches the ultimate tensile or compressive strength at any location

3)Material is not as homogeneous as steel and often carries residual stresses from the casting process

4)A value of 3 to 5 is recommended for factor of safety

DUCTILE MATERIALS SUBJECT TO STATIC LOAD-STEEL

1)The indicator of failure is yield strength

2)Failure is expected to occur when the tensile or compressive stress reaches the tensile or compressive yield strength at any location

3)A value of1.5 to 2 is recommended for factor of safety to be applied on the yield strength in tension or compression

DUCTILE MATERIALS SUBJECT TO VARIABLE LOAD-STEEL

1)The indicator of failure is endurance or fatigue strength

2)Fatigue failure depends on both the magnitude of stress and the number of loading cycles

3)Fatigue strength also varies with material properties as well as other factors that are unique to the part such as:

a)Yield strength

b)Stress concentration

c)Surface finish

d)Size

e)Temperature of part

4)Fatigue failure is sudden and total, in a similar manner to the static failure of brittle materials

5)A value of 1.3 to 1.5 is recommended for factor of safety to be applied on the fatigue strength

COLUMN FAILURE BY BUCKLING

1)Members loaded in compression are likely to fail by buckling

2)Buckling is caused by elastic instability which results in large deflection of the compression member

3)Buckling load depends on

  1. Compressive load
  2. Yield strength of the material
  3. Modulus of elasticity of the material
  4. End conditions for the column, such as fixed/fixed, pivoted/pivoted, free/fixed, pivoted/fixed.

4)A factor of safety of 3 to 6 is recommended to be applied on the buckling load

5)For a given column dimension and end conditions, the Euler column formula expresses the critical unit load in terms of the slenderness ratio, the modulus of elasticity, and the end conditions constant.

6)The critical unit load expresses the loss of function load on which the factor of safety is to be applied.

PARTS SUBJECT TO CONTACT STRESSES

Parts such as cams, gear teeth, bearings, rail wheel on rail, are subject to contact stresses between the surfaces which result in local failure of the surface by pitting.

This is local failure caused by contact stressreachingendurance strength of the surface materialat the point of contact.

Such local failure does not render the entire machine element out of operation. Pitting is therefore a form of wear since the machine element continues to operate.

A factor of safety of 1.8 to 2.5 is recommended to be applied on the surface endurance strength.

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[1] Mechanical Engineering Design, Shigley, J., 2004, McGraw Hill, page 26

[2] Design of Machine Elements, Bhandari, V.B., page 69, Tata McGraw-Hill Publishing Company Ltd