Materials, Failure and LSFs

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Material PropertiesFailure Modes

Limit State FunctionsReferences

Structural Integrity

Day 1-3: Materials, Failure, and LSFs

Dr N.C. RentonPhD CEng MIChemE

School of Engineering, University of Aberdeen, U.K.

UCAN, Bogota, 12th-15th July, 2011 Structural Integrity Day 1-3: Materials, Failure, and LSFs





‘Safety is a state of mind ’






Outline

1 Material Properties

2 Failure Modes

3 Limit State Functions






Constitutive Relation

Figure: The stress-strain relation for Carbon Steels


M i l P i





Crack Resistance

There are two ways of representing the crack resistance of a material:

1 Energy based interpretation e.g. Toughness G , J -Integral

2 Stress field e.g. Stress Intensity Factor K :

The stress intensity factor is common for most carbon steels, and the

mode I opening equation is given by:

K I = Y σ (πa)1/2 (1)

where Y is a dimensionless function related to the crack geometry(a, 2c ), a is the crack depth, 2c is the crack length. When K I reachessome critical value, and provided the level of plastic strain around thecrack is small (small scale yielding), the crack propagates in a brittlefashion at the speed of sound. The critical value is known as K IC , oftenreferred to as the fracture toughness.


Material Properties





Corrosion Resistance

Figure: Corrosion damage to duplex SS


Material Properties






Figure: Tafel Plot (Current v/s Potential) of a Stainless Steel


Material Properties






The corrosion resistance of a material depends on a number of things:

Chemical Composition: Cr, Mo, W, Ni, Cu, N.

Presence of protective oxide film.

Plastic deformation i.e. number of dislocations per unit volume.

Crystallographic structure i.e. Ferrite (bcc), Austenite (FCC),Martensite, etc

Diffusion coefficients

All are important in determining the materials ability to avoid particularcorrosion mechanisms, and hence failure.


Material Properties





Failure Mode: Burst

The engineering system we are going to concentrate on is a steel pressurecontaining vessel. The failure mode we are going to examine iscatastrophic burst by overpressure which will provide the framework forthe course. The problem is simplified by considering only the hoop stress

σh caused by the internal pressure, and the assumption of a thin-walledcylinder. The hoop stress is then:

σh =P .D

2.t × g (D , t ,wall loss defect) (2)

where P is the internal pressure (Pa); D is the vessel diameter(m); t isthe wall thickness of the vessel where t = r 2 − r 1(m); andg (D , t ,wall loss defect) is a dimensionless function that represents anarea of wall loss through corrosion.


Material Properties



pFailure Modes


Limit State Functions

Freudenthal[1, 2] and Shinozuka[3] introduced a modelling approach of the event ’failure’ in structural reliability problems. The failure event, orlimit state, is modelled by defining a safety margin M , a scalar, where:

M ≤ 0 corresponds to failureM > 0 corresponds to safe operation

In the simplest case M is defined in terms of the capacity of the system(R ) and the demand placed on it (S ) in which case failure can be

described by: M = R − S (3)

The techniques are described in detail in [4, 5].


Material Properties



Failure ModesLimit State Functions

References

Limit State Functions

In our example, failure occurs when the hoop stress exceeds the ultimatestress σu of the steel the vessel is constructed from. The capacity R isthe ultimate stress σu and the demand S is the applied stress σh. The

safety margin or limit state function can then be written as:

M = σu − σh (4)

and hence:

M = σu −

P .D

2.t g (D , t ,wall loss defect) (5)


Material Properties



Failure ModesLimit State Functions

References

References

[1] A. M. Freudenthal. “Safety, Reliability, and Structural Design”. In:Transactions of ASCE 127.Paper No 3372 (1962), pages 304–319.

[2] A. M. Freudenthal, J. M. Garrelts, and M. Shinozuka. “The Analysisof Structural Safety”. In: Journal of the Structural Division ASCE

92.ST1 (1966), pages 267–325.

[3] M. Shinozuka. “Probability of Structural Failure under RandomLoading”. In: Journal of the Engineering Mechanics Division, ASCE

90.EM5 (1964), pages 147–170.

[4] P. Thoft-Christensen and M. J. Baker.Structural Reliability Theory

and its Applications . Springer Verlaag, 1982. isbn: 0387117318.

[5] R.E. Melchers. Structural Reliability Analysis and Prediction. 2nd.1999. isbn: 978-0-471-98771-0.


Materials, Failure and LSFs

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