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Entry

Archard’s Law: Foundations, Extensions, and Critiques

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
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Author to whom correspondence should be addressed.
Encyclopedia 2025, 5(3), 124; https://doi.org/10.3390/encyclopedia5030124
Submission received: 1 July 2025 / Revised: 22 July 2025 / Accepted: 11 August 2025 / Published: 15 August 2025
(This article belongs to the Section Engineering)

Definition

Archard’s wear law is among the first and foremost wear models derived from contact mechanics that relates key operating conditions and material hardness to sliding wear through a multifaceted wear coefficient. This entry explores the development, generalization, and critique of the Archard model—a foundational model in wear prediction. It outlines the historical origins of the model, its basis in contact plasticity, and its use of a constant wear coefficient. The discussion highlights modern efforts to extend the model through variable exponents and empirical calibration. Key limitations such as the oversimplification of wear behavior, exclusion of factors like sliding velocity, and scale sensitivity are examined through both theoretical arguments and experimental evidence. The critiques reflect the model’s constrained applicability in diverse wear conditions across varied operating conditions and material phenomena.

1. Introduction on Archard’s Wear Law

The study of wear modeling has a long and extensive history. In 1995, it was thought that wear modeling was largely unorganized; Professor Ludema and his then graduate student Meng [1] conducted an extensive review covering the work of over 5000 authors who published with Wear and Wear of Materials conferences between 1957 and 1992. They reported that there was nearly no repetition of models yielding 182 distinct equations, which collectively involved over 100 unique variables and constants. Despite the many models stemming from similar theoretical foundations and approaches—including empirical observations, basic contact mechanics and material failure theories—there was no consistent structure among the resultant formulas. Nevertheless, one of the earliest models, known as Archard’s wear law, has remained one of the most prominent approaches to estimating wear [2]. Archard’s model, developed following earlier contributions by Holm [3], proposed that wear volume is proportional to the applied load (L) and the sliding distance (s) and inversely proportional to the material hardness (H), as seen in Equation (1), where V represents the total wear volume.
V = k L s H
The above adhesive wear law can be derived following the details stated by Halling [4] and Figure 1. The wear volume per sliding distance Q = V / s for n spherically shaped asperities approximates from the worn volume as a half sphere, Q = n ( 2 / 3 π r 3 ) / 2 r = n π r 2 / 3 , which is proportional to contact area A. If p m is the yield pressure, or hardness, then the normal load is L = p m A = p m n π r 2 . Therefore, the wear volume per sliding distance is Q = L / ( 3 p m ) . Given that not all contacts produce wear, and not all asperities wear at the same rate, the wear coefficient is introduced to yield Equation (1). Originally introduced for adhesive wear, the equation has also been shown to be applicable to simple abrasive wear [4,5,6]. Further applications have extended to fretting and oxidative wear by slightly adjusting the model to include the hardness of the tribologically altered surface layer formed during wear [7]. Given its foundational role and continued relevance, Archard’s equation deserves a reevaluation using modern analysis techniques.
The proportional relationship expressed in Equation (1) relies on a dimensionless factor known as the wear coefficient, symbolized as k. This coefficient carries multiple interpretations. It reflects the following:
  • The geometric transformation from original surface asperities to the plastically deformed contact area that generates wear;
  • The relationship between yield strength and hardness;
  • The fraction of plastic deformation that contributes to material loss;
  • The likelihood that material can be removed from the contact interface;
  • The contributions of other factors (e.g., temperature, surface tribochemical activities, lubrication, etc.) not explicitly included by Equation (1) but empirically linked to wear.
While aspects (i) through (iii) can be linked to measurable properties of geometry and materials, they also involve stochasticity that warrants caution when used as a relative metric for wear resistance across materials. Differences in shape or in how a material’s yield strength relates to its hardness can affect the coefficient independently of any actual wear damage. In some instances, such as in point (iii), plastic deformation may occur without apparent material removal, resulting in measurable volume loss that does not constitute true wear. Conversely, purely elastic asperity deformation should not yield any apparent wear volume despite nonzero operating conditions; this case forces k = 0 , which may be a special case of Equation (1). Element (iv) touches on a more deterministic aspect of the model in statistical estimation of adhesive wear coefficients by integration of distribution of asperity critical junction sizes [8]. However, most wear models still rely on probabilistic approaches, especially when considering wear mechanisms beyond adhesion. Overall, the wear coefficient serves as a catch-all (v) for various relationships and is therefore highly variable.
Archard and others noted a direct proportionality between the applied load and the real area of contact when the latter is subjected to full yielding. Sliding speed was also considered a tightly controlled condition in many experiments [2]. If the velocity and contact area are assumed to remain constant, Equation (1) can be transformed into a rate-based model, shown in Equation (2), where the load is replaced by interfacial pressure (p) and sliding distance by velocity (u). This form, which effectively is derived via dividing Equation (1) by the contact area and taking a time derivative, expresses the rate at which wear depth (dr/dt) increases. However, this version for instantaneous wear should be applied carefully. In many wear tests, pressure does not remain constant, especially when significant wear has occurred. As a wear track develops, the contact area may increase, which would in turn reduce the pressure under the same applied load.
d r d t = k p u H
Following the work by Delaney et al. [9], this entry aims to garner a deeper understanding of Archard’s law via a systematic review on the theoretical foundations, extended forms, and known limitations of the model. In doing so, attention is drawn to the careful considerations one must account for when using Archard’s law for wear characterization or prediction. Modern approaches, such as machine learning, multifield modeling, and energy-based frameworks, are discussed as future directions for improved accuracy. Moreover, this entry discusses Archard’s law and its applications to typical cases of wear.

2. Model Variance

2.1. Extension and Organization of Archard’s Wear Law

Archard’s wear law—represented by Equation (1)—assumes idealized contact plasticity, meaning the contact pressure is limited to the pressure required for full plastic flow across the surface. This pressure is linked to the hardness of the softer of the two contacting materials [2,3,4]. In this context, hardness (H) refers to an idealized contact plasticity assumption. Surfaces with many microcracks and pores exhibit low resistance to frictional fatigue, and their indenter-measured hardness values can hardly reflect true material hardness under friction; this is not considered by Equation (1). Although Meng and Ludema [1] highlighted the inconsistent and varied nature of wear modeling, Goryacheva [10] proposed a more general framework that extends Archard’s model, in which the exponents applied to contact pressure and sliding velocity are allowed to vary, making the model adaptable to wider conditions. Zhu et al. [11] expanded this approach further by also introducing a variable exponent on hardness, resulting in the generalized model shown in Equation (3).
d r d t = k p α u β H γ
Exponents α, β, and γ reflect nonlinear influences of materials and testing environments to a certain degree, but as a result of this adjustment, the wear coefficient experiences fractional dimensionality, which further makes it complicated for its use as a relative quantity. Table 1 presents data adapted from Zhu et al. [11], with reference to Goryacheva [10], and organizes various models under the structure of Equation (3) [12]. The models listed either apply the original Archard framework or include modifications by changing the exponents or introducing additional terms.
As a part of a data-driven exploration of Archard-type wear laws, Delaney et al. [9] extended Table 1 by 39 additional and more recent wear studies. The 39 are a subset of 75 total reviewed metal wear studies. Of all these recently reviewed studies, Delaney et al. [9] found that 81% of the wear models used could be expressed by Equation (3). These are included in Table 2.
Since extending Archard’s wear law to include exponents alters a model with over 50 years of history at the time of Goryacheva’s publication [10], theoretical support or reasoning is needed. One justification for introducing α references Hertzian contact theory, where a cubic relationship exists in point contacts between normal load and maximum pressure [62]. This suggests that the pressure during wear may extend beyond the bounds of plastic flow, as assumed in Archard’s original formulation. Kragelsky [13] also proposed a model where linear wear rate is proportional to contact pressure raised to a power, r / s = p α , with α defined as 1 + b t . In this expression, b accounts for the microscopic geometry of the surface, and t represents a material property linked to frictional fatigue. Kragelsky explained that the model is experimentally valid for polymers such as plastics and rubbers. For dry sliding, b tends to be small, making α close to one, but in lubricated settings, α may be much greater. Several researchers listed in Table 1 and Table 2 also provided empirical justifications for using α and β . For instance, Rhee [17] observed nonlinear behavior in Teflon-based bearing materials as the operating conditions load and velocity were altered. To better fit the data, Rhee introduced exponents on these variables and added a time-dependent term. Similarly, Xue et al. [41] reported that the wear performance of self-lubricated bearings with fabric liners varied with pressure and velocity. Cayer-Barrioz et al. [23] concluded that wear on polymer fibers scaled with the square of the applied load. In many cases, these exponent-based adjustments were derived from experimental findings rather than from theoretical principles. Moore et al. [21], for example, used exponent β to express the velocity effect shown in diamond tool wear models based solely on empirical results.
Regarding the exponent γ , it is important to consider that hardness is a measure of a material’s resistance to plastic deformation and is associated with its yield strength (SY). Elastic–perfectly plastic analyses of steels in circular contact configurations suggest a typical hardness-to-yield-strength ratio (H/SY) of around 2.31, assuming hardness equals the average pressure required for full surface plastic flow. However, a value of 3.0 is often used in practice [12,63,64,65,66,67]. The relationship among hardness, yield strength, and other material properties, such as work hardening, is complex. Typical hardness–yield strength correlations often overlook factors like grain size, deformation rate, and indenter geometry [67]. Cheng and Cheng [68] explored this relationship in a dimensionless study, comparing normalized hardness (by yield strength) to normalized yield strength (by Young’s modulus) across a range of work-hardening exponents. They found a nonlinear pattern, with the ratio H/SY approaching 1.7 only when SY/E exceeds 0.1. Their findings emphasize that hardness depends on both yield strength and Young’s modulus and is especially sensitive to the work-hardening behavior of the material when SY/E is small (e.g., high-strength bearing steel). These insights suggest that exponent γ in Equation (3) could be used, to a certain extend, to capture the nonlinear relationship between hardness and the underlying material resistance to wear.

2.2. Evolution and Criticism of Archard-Type Models

Since the publication of the Meng–Ludema review [1], the field of wear modeling has continued to evolve, with new trends emerging. Goryacheva [10] suggested that the relationships among key variables in wear modeling need not be strictly linear, as seen in Equations (1) and (2) and some of the earliest wear modeling work. In the context of glass polishing and decades prior to Archard [2], Preston [69] pointed to a linear relationship between wear depth and the product of frictional force and sliding distance at constant velocity. Goryacheva [10] suggested that the exponents could vary depending on material properties, surface interactions, and test conditions. Kragelsky et al. [70] proposed a similar approach presenting a model in which the wear rate over time depends on both contact pressure and sliding velocity. Collectively, these studies indicate that wear relationships may take many forms depending on the application.
One notable finding from the reviewed literature is that only one study, conducted by Xue et al. [41], presented a wear model utilizing non-integer exponents. No other authors in the surveyed publications included exponent values other than 0 or 1 in their formulations. In contrast to earlier works summarized in Table 1, more recent studies generally retain the integer-based exponents originally used in Archard’s law. While this consistency is understandable in studies focused on characterizing wear, it has greater implications in theoretical wear modeling. Theory developed from contact plasticity with realistic assumptions provides justification for keeping α = β = γ = 1 . However, some researchers have raised questions about the universal applicability of Archard’s model; this is especially in reference to operating conditions. In dry sliding experiments, research has shown that wear coefficient varies with the product of normal load and sliding distance, suggesting that Archard’s Law may not hold under all conditions [50]. Similarly, noticeable decreases in wear rate over time during testing have been observed, indicating that wear behavior changes between the initial, middle, and final phases of the test [39]. Research on wear of magnesium alloys showed that at lower loads, oxidative, abrasive, and adhesive wear were dominant, but at higher loads, delamination wear became more prominent; at even higher loads, plastic deformation wear emerged, where permanent deformation caused hardened, brittle areas that fragmented further [35]. An approach optimizing a hybrid model incorporating an artificial neural network into the model proposed by Goryacheva [10] (no γ exponent) allowed the wear coefficient and the exponents α and β to be learned from experimental data, yielding optimized values α   =   0.257 and β   =   1.503 [71]. The nonlinear behavior achieved by the aforementioned authors challenges the linear load–wear volume relationship implied by Archard’s equation.
Archard’s model, while foundational in the sense of contact plasticity, has been widely critiqued for its reliance on a constant wear coefficient, k, which must account for a broad range of physical influences that are not explicitly represented in the equation. A key omission in Equation (1) is sliding velocity that plays a central role in tribochemical processes such as oxidative wear because of the level of frictional heating and microscopic kinetics. For example, in magnesium composites, higher sliding speeds lead to the formation of a protective magnesium oxide layer, which can be confirmed through scanning electron microscopy and energy dispersive X-ray spectroscopy analyses, resulting in a reduced wear rate—an effect not captured without allowing k to vary with velocity [72]. Researchers have proposed alternative approaches to address the limitations of a constant k. This includes models where k varies spatially with deformation energy, capturing changes in wear particle evolution across the contact zone [59]; where it varies with frictional energy dissipation, although their method’s reliance on friction coefficient introduces ambiguity, as it is not a true operating variable [73]; or, as previously mentioned, where it is modeled by an artificial neural network to vary with composite properties [71]. Supporting selection of k with machine learning improved predictive accuracy over both purely theoretical and purely data-driven models. Together, these studies underscore that the assumption of a constant wear coefficient oversimplifies the dynamic nature of wear and limits the model’s generalizability across materials and operating conditions.

2.3. Modern Approaches and Modeling Limitations in Contemporary Wear Research

Recent studies have advanced wear modeling by coupling Archard’s law or its variants with multi-physics frameworks. Shen and Ke [74] integrated electrical, thermal, and mechanical fields to model fretting wear. They captured feedback between Joule heating, contact resistance, and wear depth. Li et al. [75] embedded a thermo-mechanical energy-based wear model in finite element simulations that revealed how temperature-dependent friction alters fretting wear rates. Both author groups used the previously mentioned energy dissipation wear model [73] which should better capture the positive feedback between heat generation and material degradation and performed as well as or better than the conventional Archard model [75]. Instances of coupling Archard’s law with gear mechanics have proved useful; Walker et al. [76] combined gear dynamics with lubrication and asperity contact to show how evolving wear re-distributes loads and affects transmission noise and efficiency. Using a form of Archard’s law relating wear scar depth to Hertzian line contact pressure and sliding distance, nondimensional film thickness λ was used to construct a linearly variable wear coefficient to reflect changes in wear from mixed to hydrodynamic lubrication. In an application for planetary gear systems, dynamic wear coupling showed how progressive tooth wear laws with thermal, mechanical, electrical, or lubrication physics enables more accurate system-relevant wear predictions across industrial applications [77]. Again, wear was related to Hertzian pressure and sliding distance, but the wear coefficient was measured experimentally. Chen et al. [78] developed a fully coupled elastohydrodynamic–thermal wear model for journal bearings using Archard’s law supported by damage criteria. Their modeling demonstrated that misalignment and heating produce edge-localized wear unpredicted by isothermal models—implying a spatial component to the wear coefficient.
The advent of machine learning (ML) has presented an opportunity for enhanced wear modeling. While tribologists have utilized common ML methods to regress wear data, a more integrated approach has been taken by some researchers to better integrate ML with Archard-type wear laws. The previously mentioned study by Argatov and Chai [71] employed a hybrid regression strategy in which an Archard variant (named the Archard–Kragelsky model where d r / d t = k p α u β ) was combined with a neural network that learned residual nonlinearities in composite wear data. Contact mechanics remained central while ML was used to enhance the flexibility of wear coefficient and variable exponents. In contrast, Jayasinghe et al. [79] emulated the same wear model inherently within the architecture of a neural network by designing activation functions across three hidden layers that reflect physical dependencies. Their neural network architecture was inspired by contact mechanics; however, it is difficult to attribute success in their study to this informed design. With no comparison to a conventional neural network architecture (e.g., three hidden layers all with rectified linear unit or Sigmoid activation functions), the predictive power of their model could be attributed to the capacity of the neural network itself since it is known that networks with three layers are completely capable of modeling complex, nonlinear relationships in data. It can be expected that through analyzing large amounts of wear data, proper machine learning may help create specialized variants of Archard’s law and give approximate forecasts of wear.
Zhang et al. [80] conducted a comprehensive review of both traditional and modern wear modeling approaches. They emphasized the continued prominence of the Archard model, while also highlighting its shortcomings. Specifically, they noted that the model often fails to reflect actual wear behavior as effectively as some empirical alternatives. They criticized the requirement for empirical calibration of the constant k and also pointed out that the linear relationship between wear volume and applied load does not always align with experimental data. Their assessment is consistent with Goryacheva’s earlier observations. Zhang et al. [80] also examined contemporary simulation techniques, such as the finite element method and molecular dynamics (MD). These tools offer possibilities but require careful use since adhesive wear, for instance, only emerges at length scales larger than tens of microns [81]. Below this scale, other forces—unrelated to the applied load—can significantly influence wear, deviating wear from traditional macroscopic patterns. Breakdown of atom-on-atom contact becomes the dominating interaction where bond-breaking is the governing process rather than continuum plasticity [82,83].
Recent MD wear studies reveal fundamental differences in wear mechanisms than those assumed by Archard. As previously discussed, Archard’s law assumes a well-defined material hardness and continuum contact area. These assumptions cannot hold in MD simulations where single-asperity contacts fail by discrete atomic events [82,83]. As is the case with extreme loads and velocities on the macroscale, the linear relationship between wear volume and load breaks down at the atomic level since the number of displaced atoms grows nonlinearly with increased normal force [84]. The atomistic nature of MD simulations shows a fundamental difference to modeling the same wear mechanisms as Archard’s law.
Molecular dynamics also faces immense computational and scalability challenges. The timescale of MD simulations is 10 orders of magnitude shorter than that of a typical wear experiment. To achieve any wear between contact asperities, MD simulations can run with sliding velocities up to 100 m/s [85], which limits their ability to generalize to macroscale applications. The short time (and length) scale also presents issues for the effects of wear debris agglomeration and surface evolution. Despite these challenges, simulation-based models show promise. Zhang et al. [80] noted that improvements in modeling contact geometry, material deformation, and surface texture could further enhance predictive accuracy—echoing earlier observations about the multifaceted nature of the wear coefficient k.
Delaney et al. [9] conducted a calibration study where a volumetric form of Equation (3) was fit to wear data collected from diverse wear studies. Of the 75 wear experiments reviewed, only 39 presented their data in a manner sufficient to support the calibration task. The fitted exponents were plotted and clustered using a Gaussian Mixture Model into two groups: one reflecting models resembling the original Archard model, and the other reflecting variant models, named the Alternate cluster. Regarding the previously mentioned loss of its dimensionless quality in Equation (3), a histogram of calibrated wear coefficients is provided in Figure 2. For extreme fits (i.e., those belonging to the Alternate cluster), k values are pushed to extremes and deviate from the approximate log-normal distribution observed by fits clustered near the classic Archard model (i.e., α = β = γ = 1 ).
Delaney et al. [9] revealed that material hardness as the sole proxy for material response may be insufficient for two reasons. In calibrated models that remained near the Archard model, there were many instances where the lack of any correlation between wear volume and material hardness resulted in poor fits ( R 2 < 0.5 ). Alternatively, in many cases where material treatments designed to increase hardness were tested against a baseline, extremely nonlinear fits (on average γ 7 ) were observed, resulting in unrealistic wear models. This analysis also suggested several issues for attention in enhancing wear modeling:
  • Surface evolution during wear resulting from complex, interconnected impacts of phenomena arising from a sliding interface: frictional heating leading to high flash temperatures, thermally induced deformations, and changes in material properties; wear fragment behavior and asperity fatigue; and tribochemical degradation;
  • The transition and entwinement of wear mechanisms as a function of operating conditions and material properties;
  • The lack of progressive wear characterization and measurement;
  • The lack of consistency in wear data measurement, structure, and representation;
  • The role of friction.
Delaney et al. [9] also suggested approaches for Archard’s law non-dimensionalization.

3. Conclusions and Prospects

Archard’s wear law remains a reasonably widely used model for wear behavior analyses, wear characterizations, and numerical simulations of tribological processes. However, decades of research have revealed its limitations—particularly the usage of a constant wear coefficient, the linear dependence on key variables such as load and velocity, and over-reliance on hardness to represent material plasticity. Wear behavior is complicated in nature, material-dependent, and sensitive to operating conditions. The generalization of Archard’s model through variable exponents offers a broader, more flexible framework but demands careful calibration and theoretical justification.
Recent advances have sought to overcome these limitations through two complimentary strategies: multi-physics coupling simulations and augmenting machine learning with physical modeling. Incorporating wear in multi-physics modeling approaches treats wear as a dynamic process coupled with co-evolving pressure, temperature, lubrication, and material property changes. This rebrands wear as not just an outcome but also a driver of system behavior and contributor in system-wide feedback loops. These models have heavy computation requirements but introduce causal depth to wear modeling that the Archard model lacks. Additionally, integration of wear models into a machine learning architecture reflects a shift from a curve fitting exercise to generalization constrained by physics. Embedding a physical wear law into a loss function or network architecture regulates network inferences and balances the flexibility of a highly capable neural network with law-based reasoning.
Prospects for the future of wear modeling involve the recontextualization of Archard’s law rather than its dismissal. While its role as a predictive model has been heavily criticized, it may serve more useful as a constraining boundary condition for more advanced formulations. Its function may serve as a foundational scaffold that guides the structure of data-driven models, supports interpretability, and facilitates integration within a hybrid modeling framework. Future success in wear modeling will include a thoughtful interplay between physical laws that lack complete generality and highly capable, data-driven ML methods that lack physical constraint, with the critical aspect being the integration of the two, because by themselves they prove insufficient for practical engineering activities.

Funding

This research was funded by the National Science Foundation Graduate Research Fellowship, Grant No. DGE-2234667, and the Army Research Laboratory under Cooperative Agreement Numbers, Grant Nos. W911NF-20-2-0230 and W911NF-20-2-0292.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Illustration of asperity contact under applied load L and resulting approximation of wear volume depicted by the red shaded region within the dashed contact radius.
Figure 1. Illustration of asperity contact under applied load L and resulting approximation of wear volume depicted by the red shaded region within the dashed contact radius.
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Figure 2. A distribution of dimensional wear coefficients grouped by unsupervised machine learning clustering. (Adapted with permission from ref. [9]. Copyright 2025 American Society of Mechanical Engineers).
Figure 2. A distribution of dimensional wear coefficients grouped by unsupervised machine learning clustering. (Adapted with permission from ref. [9]. Copyright 2025 American Society of Mechanical Engineers).
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Table 1. Wear models including exponential constants for pressure (load), sliding velocity (distance) and hardness as organized by Goryacheva [10]. (Adapted with permission from ref. [11]. Copyright 2007 American Society of Mechanical Engineers).
Table 1. Wear models including exponential constants for pressure (load), sliding velocity (distance) and hardness as organized by Goryacheva [10]. (Adapted with permission from ref. [11]. Copyright 2007 American Society of Mechanical Engineers).
Author (Year) α β γ Additional Terms UsedWear Mechanisms
Holm [3] (1946)111 Adhesion
Archard [2] (1953)111 Adhesion
Kragelsky [13] (1965)>110 Fatigue
Rabinowicz [14] (1965)111 Abrasion/fretting
Lewis [15] (1968)110 Adhesion of filled PTFE and piston rings
Khrushchev and Babichev [16] (1970)111 Microcutting of metals
Rhee 1 [17] (1970) α β 0Exponential function of t Adhesion with thermal effects
Lancaster [18] (1973) 110Includes wear rate correction factorsFilled thermoplastics and filled PTFE
Larsen-Basse [19] (1973) 110Defined in terms of impact frequencyThermal fatigue and carbine polishing
Hurricks [20] (1976)110 Fretting
Moore et al. [21] (1978)11.80 p = p (rock volume removed/distance)Wear of diamond inserts and rotary drag bits
Luo et al. [22] (2005)011Normal stress between tool flank face and work pieceAdhesion/abrasion of cutting tool flank
Cayer-Barrioz et al. [23] (2006)210Molecular weightAbrasion of polymeric fibers
1 published several experimental fits where α and β vary from 0.43 to 1.6 and from 0.6 to 1.6, respectively.
Table 2. Recent Archard-type models following the organization of Goryacheva [10]. (Adapted with permission from ref. [9]. Copyright 2025 American Society of Mechanical Engineers).
Table 2. Recent Archard-type models following the organization of Goryacheva [10]. (Adapted with permission from ref. [9]. Copyright 2025 American Society of Mechanical Engineers).
Author (Year) α β γ Additional Terms UsedWear Mechanisms
Wang et al. [24] (1990)110 Effect of Material Hardening on Wear Rate
Siniawski et al. [25] (2003)111 Wear Development of Boron Carbide Coatings
Bartha et al. [26] (2005)011Proportional to mass loss WHigh-Precision Machining
Hegadekatte et al. [27] (2005)110 Archard’s Law as a Foundation of Wear Simulation
Li et al. [28] (2005)110 Wear Effects of Microstructure
Bressan et al. [29] (2006)111 Wear-Resistant Steel Coating
Sen and Sen [30] (2008)110 Wear of Niobium Carbide Coating
Sen and Sen [31] (2009)110 Wear of Boronizing and Chromizing Steel
Sun et al. [32] (2009) 110 Wear of Steel on Ceramics
Andersson et al. [33] (2011)111 Wear Simulation Validation
Barunovic et al. [34] (2012)110 High-Load, Diesel-Lubricated Sliding
Taltavull et al. [35] (2013)110 Wear Resistance of Magnesium alloys
Gunes et al. [36] (2014)110 Cryogenic Treatment to Improve Wear Resistance
de Castro et al. [37] (2016)111 Wear Performance of Automobile Lubricants
Furustig et al. [38] (2016)110 Wear Simulation Validation
Xi et al. [39] (2017)111Substitution of Hardness with Yield StressWear Simulation Validation
Jia et al. [40] (2018)110Negative sign introduced to indicate direction of wearRotary and Linear Wear Modeling
Xue et al. [41] (2018)mn0 Simulation of Wear Failure
Yu et al. [42] (2018)111 Wear Life of Deep-Groove Ball Bearings
Liu et al. [7] (2019)111 H = H T T S (Peak Load, Stiffness, Wear Depth)Improved Modeling of Fretting Wear
Cross et al. [43] (2020)110 Ratcheting Wear of Cobalt-Chromium
Joshua and Babu [44] (2020)010Sliding distance expressed as product of angular velocity, disk radius, and timeBearings used in Automobile and Railway Industries
Moghaddam et al. [45] (2020)110 Effect of Carbide-free Bainitic Microstructure on Oxidation-dominated Wear
Özkan et al. [46] (2020)110 Friction Reduction for thin-film coatings
Bildik and Yaşar [47] (2021)m = 1n = 01 Manufacturing Process Impact on Wear Resistance
Kaelani and Syaifudin [48] (2021)111 Mathematical Modeling of Wear
Liu, et al. [49] (2021)110 Mining and Agriculture
Reichelt and Cappella [50] (2021)111 Validity of Archard’s Law
Tabrizi et al. [51] (2021)111Proportional to height of asperity peaks, surface roughness, squared tangent of asperity slope, and inversely to difference in interfacing surface hardnessesExtension of the Archard Model
Li et al. [52] (2022) 110 Wear Life of Metal Rubbers
Morón et al. [53] (2022)110 Dry and Lubricated Borided Bearing Steel Wear
Mosbacher et al. [54] (2022)110 Effect of Heat Treatment on Tribological Performance
Rudnytskyj et al. [55] (2022)110 Wear Simulation Validation
Torkamani et al. [56] (2022)110 Damage Mechanisms in Modern Machinery
Birleanu et al. [57] (2023)110 Improved Tribological Properties of Composites
Yan et al. [58] (2023)111 Surface Texture to Reduce Sliding Wear
Choudhry et al. [59] (2024)111 K = K ( E d e f o r m a t i o n ) Improved model of Adhesive Wear
Li et al. [60] (2024)110 Wear Influence of Hardness and Spherical Carbides
Wu et al. [61] (2024)110 Wear Life of Bearing Steel
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Delaney, B.; Wang, Q.J. Archard’s Law: Foundations, Extensions, and Critiques. Encyclopedia 2025, 5, 124. https://doi.org/10.3390/encyclopedia5030124

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Delaney B, Wang QJ. Archard’s Law: Foundations, Extensions, and Critiques. Encyclopedia. 2025; 5(3):124. https://doi.org/10.3390/encyclopedia5030124

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Delaney, Brian, and Q. Jane Wang. 2025. "Archard’s Law: Foundations, Extensions, and Critiques" Encyclopedia 5, no. 3: 124. https://doi.org/10.3390/encyclopedia5030124

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Delaney, B., & Wang, Q. J. (2025). Archard’s Law: Foundations, Extensions, and Critiques. Encyclopedia, 5(3), 124. https://doi.org/10.3390/encyclopedia5030124

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