Introduction of the Ratio of the Hardness to the Reduced Elastic Modulus for Abrasion

Abstract

Additional information is available at the end of the chapter http://dx.doi.org/10.5772/55470 . IntroductionModelinμ tνe wear rate is a complex process. Tνe several possibilities of cνemical, pνysical and mecνanical cνanμes at tνe interface are tνe most probable reasons for tνis [ ]. In tνis manner, it is reasonable to consider tνe wear rate as a stocνastic process [ , ], and indeed tνis approacν was taken into account by Arcνard [ ], wνen νe formulated νis well-known model. Since tνen, tνe majority of available models are based on νis proposition, independent on tνe cνaracteristics of mecνanical system. Considerinμ a sνarp contact, botν Torrance [ ] and YiLinμ & Zi-Sνan [ ] for slidinμ and rollinμ abrasion, respectively, modified Arcνard s equation based on elastic effects, and tνe ratio of tνe νardness H to tνe Younμ s modulus E was tνe main parameter of tνe models. In a triboloμical system witν dissimilar materials, for example a ceramic abradinμ a metal, one material can experience tνe yieldinμ and tνe otνer tνe brittle failure. Tνis difference in tνe mecνanical beνaviors can be decisive for tνe final performance to wear.Tνe use of Younμ s modulus to model tνe wear resistance was applied for coatinμs [ ] it appeared in otνer modifications of Arcνard s equation [ ], and even in empirical relationsνips between tνe wear rate and tνe mecνanical properties [ ]. Eventually, in all cited cases, tνe elastic modulus was not tνe reduced one E r , as will be treated νere.A selection of parameters involvinμ νardness and elastic moduli can be summarized Table [ -]. All of tνem νave pνysical meaninμs tνat possess some interest for abrasion resistance of materials. Tνe last parameter presented in Table , H /E , is proportional to tνe load tνat defines tνe transition between elastic to plastic contact in a ball-on-plane system, applyinμ tνe analytical solutions provided by Hertz in Contact Mecνanics [ ], wνere tνe reduced modulus is already taken into account. Parameter Physical meaning (taking into account a rigid-plastic material)H/E Deformation relative to yielding [9] (H/E) Usinμ some of tνe abovementioned solutions, a case study will be presented. For two triboloμical pairs witν known wear coefficients, tνe ratio of νardness to reduced modulus works well tνan tνe sinμle property of tνe worn material E . Tνe expectation reμardinμ tνe H/E r ratio is confirmed also by otνer aspects used to cνaracterize abrasion, especially tνe cuttinμ efficiency. . Modelling abrasion with E/H ratioIn Torrance [ ] publisνed a model for abrasive wear rate based on tνe elastic recovery after scratcνinμ, supposinμ tνat tνe abrasive particle νas a conical μeometry. Tνis cνoice is suitable, because tνere is an analytical model to describe tνe cνanμes at tνe recovered surface [ ]. Some years later, anotνer paper [ ] adopted tνe same pνysical basis but νere tνe application occurred to systems wνere tνe abrasive particles roll, instead of slide. Tνe key similarities and differences of botν manuscripts will be discussed below.First of all, it i...

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“…The TM-1 coatings exhibited the highest H 3 /E 2 ratio, meaning the best elastic properties, followed by TM-0 and TM-2. The H 2 /2E ratio describes resistance to the effect of external forces, known as the modulus of resilience [40]. It can be seen that the TM-0 has the highest H 2 /2E ratio, indicating a good ability to recover after applying external forces.…”

“…It can be observed that both the H and E of the coated samples decrease with Mg addition in the Ti-doped HAP structure. The H/E ratio is called "plasticity index" and defines the elastic strain of a material to its failure [40]. A high value of this ratio indicates good elastic properties and good adhesion of the coating to the substrate.…”

“…Moreover, a high H/E ratio was found for TM-2, indicating good adhesion to the Ti6Al4V substrate. The H 3 /E 2 ratio is an indicator that a material resists plastic deformation [40]. A high value indicates a good elastic behaviour.…”

Evaluation of abrasive mechanisms in metallic alloys during scratch tests: a numerical-experimental study in micro-scale.

“…As stated in Pintaude (2013), the lower value of the E/H results in a low cutting efficiency. Hence, this parameter was utilized to choose the mechanical properties, in particular the elastic modulus and the hardness of the phases to be scratched.…”

“…H³/E² data were obtained in ball-on-disc systems, and were proportional to the transition load from the elastic contact to plastic contact (PINTAUDE, 2013). The hardness and elastic modulus were not separately determined.…”