Skip to main content Accessibility help
×
Home
  • Print publication year: 2011
  • Online publication date: June 2012

8 - Failure theories

from Part II - Mechanics

Summary

Inquiry

How would you safely design a tibial insert of a total knee replacement that is known to experience a complex loading state with a normal stress component that is on the order of the uniaxial strength for this material?

The inquiry posed above represents a realistic design challenge that one might face in the field of orthopedics. Many of the tibial components used in total knee arthroplasty utilize ultra-high molecular weight polyethylene with a uniaxial yield stress on the order of 20 MPa; yet, the contact pressures for many of the clinical designs exceed this value. In order to assess the likelihood for failure owing to yield or plastic deformation, it is important to calculate the effective stress that provides a scalar representation of the multiaxial stress state acting on the implant. It is the effective stress that must be compared to the uniaxial yield strength as an assessment for the factor of safety against failure. Furthermore, localized plastic damage due to the presence of a notch or stress concentration can serve as a nucleation site for cracks if the component undergoes cyclic loading conditions. All of these factors must be considered when designing the implant.

Overview

The process of material failure depends upon the stress state of the system as well as whether its microstructure renders it ductile, brittle, or semi-brittle. In general, ductile materials yield before fracture while brittle materials fracture before yield. A semi-brittle system offers a small amount of plastic or permanent deformation prior to fracture. In the broad spectrum of materials behavior, metals are generally considered strong, tough, and ductile; ceramics are known to be strong in compression but weak in tension, and are notoriously brittle; and polymers are usually compliant, resilient, and highly sensitive to strain rate. Composites and tissues are typically anisotropic and are highly dependent upon the distribution of constituents. The most commonly employed mechanical test for material characterization is the uniaxial tensile test, which provides several important material properties including elastic modulus, yield strength, ultimate tensile strength, fracture stress, energetic toughness, and ductility (as shown in Figure 8.1).

Related content

Powered by UNSILO
References
Bartel, D.L.Bicknell, V.L.Wright, T.M. 1986 The effect of conformity, thickness and material on stresses in ultra high molecular weight polyethylene components for total joint replacementsJournal of Bone and Joint Surgery 68 1041
Dowling, N.E. 2007 Mechanical Behavior of MaterialsUpper Saddle River, NJPearson Education
Gerber, T.L.Fuchs, H.O. 1968 Analysis of non-propagating cracks in notched parts with compressive mean stressJournal of Materials 3 359
Hill, R. 1950 The Mathematical Theory of PlasticityOxford, UKClarendon Press
Holm, D.K.Blom, A.F.Suresh, S. 1986 Growth of cracks under far-field compressive loads: Numerical and experimental resultsEngineering Fracture Mechanics 23 1097
Hubbard, R.P. 1969 Crack growth under cyclic compressionJournal of Basic Engineering 91 625
Inglis, C.E. 1913 Stresses in a plate due to the presence of cracks and sharp cornersTransactions of the Institute of Naval Architects 55 219
Kausch, H.H. 1978 Polymer FractureBerlinSpringer-Verlag
Peterson, R.E. 1959 Notch SensitivityMetal FatigueSines, G.Waisman, J.L.New YorkMcGraw-Hill
Peterson, R.E. 1974 Stress Concentration FactorsNew YorkWiley
Pruitt, L.Koo, K.Rimnac, C.M.Suresh, S.Wright, T.M. 1995 Cyclic compressive loading results in fatigue cracks in ultra high molecular weight polyethyleneJournal of Bone and Joint Surgery 13 143
Pruitt, L.Suresh, S. 1993 Cyclic stress fields for fatigue cracks in amorphous solids: Experimental measurements and their implicationsPhilosophical Magazine A 67 1219
Schigley, J.E.Mischke, C.R. 1989 Mechanical Engineering DesignNew YorkMcGraw-Hill
Sines, G.Waisman, J.L. 1959 Metal FatigueNew YorkMcGraw-Hill
Suresh, S. 1998 Fatigue of MaterialsCambridge, UKCambridge University Press