JOURNAL OF MATERIALS SCIENCE 25 (1990) 1050-1057 Failure of acrylic bone cements under triaxial stresses A. SILVESTRE, A. RAYA, M. FERNANDEZ-FAIREN, M. ANGLADA, J. A. PLANELL Departamento de Ciencia de los Materiales e Ingenierfa MetaltJrgica, Escuela Tecnica Superior de Ingenieros Industriales de Barcelona, Diagonal 647, 08028-Barcelona, Spain Bone cements work under complex triaxial states of stress between the prosthesis and the bone. However, no failure criteria have been formulated for such materials. In the present work two acrylic bone cements have been tested under triaxial stresses up to failure and it has been shown that they behave following the Coulomb-Mohr criterion. Tests have been carried out with moulded thick-wall cylindrical hollow specimens. The samples were unidirectionally compressed whilst a constant internal pressure was provided. Although weaker, one of the bone cements exhibits a similar behaviour to industrial polymethylmethacrylate (PMMA). The different behaviour of these bone cements cannot be related to porosity, which ranges from 1 to 4% in both materials, nor to their different molecular weight. It has been shown that the different morphologies of the bone cement PMMA powders may account for their different mechanical behaviour. It seems that a more homogeneous distribution of sizes, ranging from 10 to 50 {lm, and shapes (practically spherical) gives rise to a material which behaves in a similar way to industrial PMMA. 1. Introduction Since Charnley [1, 2] introduced polymethylmethacry- late (PMMA) in the mid 1950s as bone cement for total hip replacements, this technique has become widely used in orthopaedic surgery. The acrylic bone cement works as a mechanical interlock between the implant and the bone by distributing the loads evenly. Despite the efforts made in investigating their mech- anical properties, there are still some aspects which remain obscure. A good example is the absence of information in the literature on their mechanical behaviour under biaxial or triaxial loading conditions [3], including the evaluation of some failure criteria. The importance of such data is obvious as the implanted bone cement works under complex multi- axial stresses and it is commonly accepted that its failure may lead to the loosening of the implant [4-7]. At present the unidirectional mechanical properties of bone cements are well understood, for reviews see [3, 8], and they can be interpreted in terms of their microstructural features. The most important are: (a) the distribution of sizes and shapes of the initial PMMA powder; (b) the porosity of the cement induced mainly by air entrapment during the hand mixing stage: (c) the incomplete mix of the initial PMMA powder and the polymerized monomer: (d) the barium sulphate particles distributed in the initial PMMA powder: (e) the increase in molecular weight due to the polymerization of the monomer around the PMMA powder; and (f) the folding and body fluid inclusions produced during the cement injection in the bone cavity. As a consequence, bone cements can be treated as isotropic, heterogeneous, porous and brittle 1050 materials. All these features support the idea that bone cements under a triaxial state of stress could follow the Coulomb-Mohr failure criterion. This criterion has been widely used in soil and rock mechanics [9] and in the study of fracture of isotropic brittle materials [10], and it has also yielded good results in polymers [11-14] and specifically in industrial PMMA [15, 16]. The Coulomb-Mohr criterion states that mechan- ical failure takes place when the shear stress r on a plane reaches a critical value which is a linear function of the normal stress on that plane: r = C + 0' N tan <I> (1) where r = shear stress at failure, 0' = normal stress to the plane of failure, C = cohesion of the material and <I> = angle of internal friction of the material. Figure I shows the graphical method of evaluating the criterion by drawing Mohr's circles corresponding to the failure triaxial (principal) stresses and then draw- ing the common tangent to all of them which will define the intercepts (C cotg <1>, 0) and (0, C) from which C and <I> can be determined. In terms of prin- cipal stresses, Equation I becomes 0'1(1 - sin <1» 2C cos <I> 0' 3 (1 + sin <1» = I 2C cos <I> (2) 0'1 and 0'3 are used to draw the Mohr's circles and correspond to the failure stresses which will be experi- mentally measured. It should be noticed when com- paring with other authors [10, 15] that in this work tensile stresses are taken as negative, whilst compress- ive stresses are taken as positive. 0022-2461/90 $03.00 + .12 © 1990 Chapman and Hall Ltd.