Hysteresis loops predicted by isoenergy density theory for polycrystals. Part I: fundamentals of non-equilibrium thermal–mechanical coupling effects

When a polycrystal is stressed or strained at fifty percent of the corresponding yield value, damage will be inflicted non-homogeneously in the material due to the fact that the stress and/or strain distribution is non-uniform even if isotropy and homogeneity are assumed for the initial microstructure. This effect will be cumulated for each cycle of the load if the applied stress or strain is repeated continuously. Nucleation of microcracks can eventually lead to the propagation of a macrocrack.The process of damage accumulation in fatigue is defined to be sufficiently slow such that inhomogeneity of material behavior created by loading is a significant factor that can not be arbitrarily dismissed without a good reason. What this means specifically is that the difference of the stress and strain behavior at each point in a fatigue specimen must be accounted for in the analytical model in order to predict the correct cumulative effect. Such a requirement translates into a non-equilibrium formulation where the constitutive relations for each point and loading cycle must be determined separately. In this sense, the true problem of fatigue cannot be completely treated by the classical continuum mechanics approach that is limited to equilibrium mechanics for a closed system. Having said this, the isoenergy density theory will be applied to estimate the hysteresis loops of a hour-glass profile cylindrical bar specimen as recommended by the American Society for Testing and Materials (ASTM) for low-cycle fatigue.The work will be divided into two parts. Part I will cover the fundamentals of a non-equilibrium theory where the continuum elements are finite in size; they do not vanish in the limit. Therefore, size effects are immediately encountered as a function of time. General expressions for the rate change of volume of these elements with surface area are derived such that they can be computed from the nine displacement gradients. These elements can differ in size and must fit together without discontinuities or gaps to form the continuum. The condition of isoenergy energy density is invoked such that the size of these individual elements under large and finite deformation and rotation can be determined without loss in generality. The existence of such a space having the property of the same isoenergy density in all directions is thus proved. This enables the establishment of the one dimensional energy state with that in three dimensions without restriction, the absence of which has prevented the development of a complete non-linear theory of mechanics that can be solved in a direct fashion in contrast to the inverse method of assuming the displacement field. Illustration is provided for deriving the constitutive relation incrementally for a given location for the hour-glass specimen made of 6061-T6 aluminum. Once the specimen is loaded, each material point will follow a different stress and strain curve according to the local displacement rate. Hence, the method applies to material with non-homogeneous microstructure if their individual expressions can be assessed and fed into the computer.Part II computes for the non-equilibrium temperature and an entropy-like quantity that can be positive and negative. This implies that the system can absorb or dissipate energy with reference to the surrounding. Additional data for hysteresis loops are given for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium. Accumulation of the local hysteresis energy per cycle is found to be the highest near the surface of the uniaxial specimen where load symmetry prevails. This is a consequence of the difference in accumulation of the energy density due to distortion in contrast to dilatation at the specimen center. This is why fatigue cracks tend to nucleate near the specimen surface, at a small distance towards the interior. Another distinct feature of fatigue is that the non-equilibrium temperature is found to oscillate about the ambient temperature while the local stress states fluctuate between tension and compression. This temperature reversal behavior is typical of non-equilibrium behavior and also occurs under monotonic loading. The space and time variations of the dissipated energy density for different materials are found to be related to the initial monotonic energy density or area under the true stress and true strain curve.What will be demonstrated is that no special consideration need to be made when applying the isoenergy density theory for analyzing the nucleation of micro and macrocracks in addition to failure of the specimen. Crack nucleation under fatigue is assumed to occur when the total hysteresis energy reaches a critical value. It is possible to establish a relation between the average hysteresis energy per cycle and the number of cycles to failure. The proposed method requires only a knowledge of the initial monotonic energy density curve for a given material. Predicted results for the fatigue of cylindrical bar specimens with hour-glass profile are given and they can be found in Part II of this work.     

Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy

Internal state variable rate equations are cast in a continuum framework to model void nucleation, growth, and coalescence in a cast Al–Si–Mg aluminum alloy. The kinematics and constitutive relations for damage resulting from void nucleation, growth, and coalescence are discussed. Because damage evolution is intimately coupled with the stress state, internal state variable hardening rate equations are developed to distinguish between compression, tension, and torsion straining conditions. The scalar isotropic hardening equation and second rank tensorial kinematic hardening equation from the Bammann–Chiesa–Johnson (BCJ) Plasticity model are modified to account for hardening rate differences under tension, compression, and torsion. A method for determining the material constants for the plasticity and damage equations is presented. Parameter determination for the proposed phenomenological nucleation rate equation, motivated from fracture mechanics and microscale physical observations, involves counting nucleation sites as a function of strain from optical micrographs. Although different void growth models can be included, the McClintock void growth model is used in this study. A coalescence model is also introduced. The damage framework is then evaluated with respect to experimental tensile data of notched Al–Si–Mg cast aluminum alloy specimens. Finite element results employing the damage framework are shown to illustrate its usefulness.     

Multiscale evaluation of microstructural worthiness based on the physical–analytical matching (PAM) approach

By selecting the appropriate spatial and temporal variables, physical abnormalities at the microscale can be limited to the essentials such that effective analytical solutions can be made available and identified with high resolution TEM and SEM micrographs. A catalogue of physical–analytical pairs can be stored electronically for the evolution of material damage from micro (or nano) up to macroscopic failure. High speed digital processing can organize such information and make forecast on potential failure in the cyberspace. The micro/macro line cracking model is used to illustrate the use of the PAM (physical–analytical matching) technique although it is still at the early stage of development. Three essential parameters describing the inhomogeneity of the material serve as the basis of the approach while specific microstructural details can be accounted for by using the incidental variables as programmed by PAM in the future. Demonstration is made by using the dual scale micro/macro line crack model where closed form asymptotic solution can be obtained from singularity representation. No generality is lost from the line crack configuration. This is analogous to taking the shape of an atom to be spherical since the exact shape is not relevant. The essential quantities are the energy density and characteristic length associated with the equivalent crack length defined with reference to the spatial and temporal variables under consideration.For a macroscopic tensile specimen containing a micro/macrocrack, multiple microcracking patterns are generated. A priori assumptions related to the grain geometries and/or cohesive force laws to create branching will not be made. Instead, values of the essential parameters are selected to obtain multiple minima of the volume energy density functions. These minima are very closely spaced. This implies that the initiation of multiple microcracking is probable even though dynamic effects are not present. This is in contrast to macrocrack branching where the crack velocity had to approach that of the Rayleigh wave speed. The formulation also shows that empirical approach blind folds the details of microscopic and scaling effects. The double singularity line crack model is used to illustrate that different multiple microcracking patterns can be predicted from the volume energy density fracture criterion that has been used extensively for examining the initiation of macrocracking. The criterion relies on identifying the locations of the stationary values of the energy density function with the potential threshold sites dominated by dilatation or distortion without assuming that the two energy density components are the linear sum, a condition invoked in linear elasticity. To reiterate, three essential parameters are defined to describe the non-homogeneous behavior of the material while two incidental variables are used for the double singularity line crack to account for specific microstructural effects. It is the ease with which asymptotic closed form solution can be obtained and identified with observed damage patterns that suggests the possibility to develop the PAM technique in the cyberspace.     

Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Tension–compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior

In-plane tension and compression experiments on copper alloy sheets (phosphor bronze) and 6000 series aluminum alloy sheets (AA6016-T4) were conducted using a specially designed testing apparatus. The apparatus is equipped with comb-type dies so that stress–strain curves of a sheet specimen subjected to tension followed by compression, and vice versa, can be measured without buckling of the specimen, as well as those for monotonic tension and compression. A difference was observed in the flow stresses between tension and compression for the as-received copper alloy, but not for the aluminum alloy. Moreover, stress reversal tests, such as tension followed by compression and compression followed by tension, were carried out in order to measure the Bauschinger effect. In the second part of the experiment, bending moment–curvature diagrams were measured for the as-received and pre-stretched specimens. The bending moment–curvature diagrams were compared with those calculated using the stress–strain curves obtained from the tension–compression tests, and were in good agreement with those calculated with the tension–compression asymmetry and the Bauschinger effect correctly reproduced.     

A methodology for thermomechanical fatigue crack growth testing in MMCs

This paper describes the experimental techniques used in an investigation of the crack growth characteristics of a four-ply, unidirectional, silicon carbide fiber reinforced, titanium matrix composite (SCS-6/Ti–6Al–2Sn–4Zr–2Mo) subjected to thermomechanical fatigue. A mechanical test system was assembled which is capable of conducting fully automated, computer-controlled thermomechanical fatigue crack growth tests. The system is able to simultaneously impose operator-defined arbitrary mechanical and thermal histories on the specimen. Crack lengths in single-edge tension [SE(T)] or middle tension [M(T)] specimens are measured by the direct-current electric potential method and optically using a unique telemicroscope system. A series of isothermal, in-phase and out-of-phase crack growth tests was conducted to obtain baseline data for material modeling purposes. The test temperatures ranged from 150°C to 538°C, and the highest thermal frequency was 0.0083 Hz.     

Thermal/mechanical damage of 6061-T6 aluminum tensile specimen

As a 6061-T6 aluminum coupon specimen is stretched, energy is being converted from mechanical work to heat. This irreversible process of material damage is detected experimentally by measuring the change in surface temperature. Contrary to the ordinary notion that the material would heat up when loaded, it actually cools before returning to the ambient condition. The recovery time was approximately 26 sec for a displacement rate of 8.467·10⁻⁵ m/sec and 200 sec when the displacement rate is reduced by one of magnitude. Cooling and heating is a rate dependent process. Three sets of temperature data were obtained for each of the displacement rates and they coincide with those prediced from the energy density theory that accounts for the nonhomogeneous dissipation of energy at every location in the specimen.Unlike any classical theories in mechanics, the energy density theory determines the stress and strain response of each element in the specimen only from a knowledge of the initial material stiffness and the displacement time rate. This is necessary because the local strain rates for elements near the center and edge of the specimen can differ by a wide margin. The so-called uniaxial stress and strain curve is then obtained by taking the average of all the elements. The results agreed extremely well with those measured experimentally for the 6061-T6 aluminum. Obtained analytically are also the thermal conductivity coefficients that are loading rate dependent and anisotropic in character due to stretching in the longitudinal direction. Their values tend to stabilize beyond the cooling/heating period.     

Mechanics and physics of energy density theory

As a departure from the classical continuum mechanics approach, irreversible material behavior is uniquely identified with the exchange of surface and volume energy density through the rate of change of volume with surface area. This provides an one-to-one correspondence between the uniaxial and multiaxial stress or energy state. Equivalent uniaxial stress and strain response can thus be determined for each material element that undergoes damage by permanent deformation and/or fracture. Discussed in detail are the applications of surface energy or volume energy with continuum mechanics theories for analyzing failure in contrast to the strain energy density that analyzes stress and failure simultaneously. In particular, the results for the progressive damage of a slowly moving crack are presented and compared with those obtained from the theory of plasticity. It is shown that the neglected of dilatational energy in plasticity results in inaccurate prediction of the state of affairs near the crack tip.Since the stresses and strains in the strain energy density theory are determined separately, nonlinear and finite strains may be easily included into dV/dA and incorporated into the formulation. This opens the door to a class of nonlinear problems that can be solved directly even for finite and large strains including energy dissipation.     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．     

Mathematical construction of a Reissner–Mindlin plate theory for composite laminates

A Reissner–Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner–Mindlin theory with an excellent accuracy comparable to that of higher-order, layer-wise theories. The present work is extended from the previous theory developed by the writer and his co-workers with several sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner–Mindlin model; (b) the semi-definite programming technique is used to seek the optimum Reissner–Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner–Mindlin model and the second-order asymptotical model can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first-order shear-deformation theory, demonstrating that the present theory has an excellent agreement with the exact solution.     

Fatigue characteristics of ‘bead-on-plate’ of aluminum and Al---Zn---Mg alloy

Fatigue life of ‘bead-on-plate’ on commercially pure aluminum and Al---Zn---Mg alloy have been investigated. In both cases, the fatigue life of ‘Bead-on-Plate’ specimen was drastically reduced. But when the same weld-bead was flushed off, a marginal improvement in fatigue life was observed. For Al---Zn---Mg alloy, the post weld heat treatment was less effective than flushing of weld-bead for improving the fatigue life of welded specimens. Results are analyzed with the help of S-N diagrams and microphotographs.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

Micromechanical study of formation and evolution of martensite for Cu–Al–Ni single crystal by moiré interferometry

The basic properties of pseudoelasticity of Cu–Al–Ni single crystal are studied to analyze the morphology associated with the formation and evolution of martensite and the shape memory recovery process at different temperatures. Use is made of a multifunctional macro–micro moiré interferometry measurement system. The β₁ to β₁^′ phase changes are identified with the stress-induced transformation of a Cu–13.7%Al–4.18%Ni (wt%) alloy. The invariant plane between the martensite and the parent phase is shown directly by fringe patterns. It is found that martensite appears in the shape of bands or thin plates on the surface of the specimen. The formation of martensite is a very rapid process and martensite ‘jumps' out until the specimen is completely transformed into a single variant. The results reveal the mechanism and process of stress-type and temperature-induced martensitic transformation.     

A heuristic approach to microcracking and fracture for ceramics with statistical consideration

Microcracking damage and toughening are examined for ceramics. These effects have been found to depend on the material microstructure and macrocrack growth. Isotropic damage, attributed to random distribution of microcrack location, length and orientation can be associated with a disordered microstructure and a non-uniform residual stress field. When the applied stress is the main cause of cracking, the microcrack distribution is no longer random such as a system of quasi-parallel cracks. To highlight the effect of crack interaction, discrete models are advanced where damage is simulated by a distribution of microcracks. The dilute concentration assumption is invoked to simplify the analysis.The two-dimensional discrete model is based on a phenomenological approach that is statistical in character. Interactions of microcracks and with a macrocrack are considered by means of a boundary element technique (A. Brencich, A. Carpinteri, Int. J. Fracture 76 (1996) 373–389; A. Brencich, A. Carpinteri, Eng. Fract. Mech. 59 (1998) 797–814) where both isotropic and anisotropic damage could be treated. Comparisons with other results are made to show that the model can be applied to analyse the fracture behaviour of different materials.     

Size effect of cylindrical specimens with fatigue cracks

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., $\text{ΔS}\text{Δa}\text{=}\text{const}$. Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

Flow of linear molecules through a 4:1:4 contraction–expansion using non-equilibrium molecular dynamics: Extensional rheology and pressure drop

In this work, non-equilibrium molecular dynamics simulations are used to generate the flow of linear polymer chains (monomer-springs with FENE potential) and a Lennard–Jones fluid (Newtonian fluid) through a contraction–expansion (4:1:4) geometry. An external force field simulating a constant pressure gradient upstream the contraction region induces the flow, where the confining action of the walls is represented by a Lennard–Jones potential. The equations of motion are solved through a multiple-step integration algorithm coupled to a Nosé-Hoover dynamics [S. Nose, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511–519], i.e., to simulate a thermostat, which maintains a constant temperature. In this investigation, we assume that the energy removed by the thermostat is related to the viscous dissipation along the contraction–expansion geometry. A non-linear increasing function between the pressure drop and the mean velocity along the contraction for the linear molecules is found, being an order of magnitude larger than that predicted for the Lennard–Jones fluid. The pressure drop of both systems (the linear molecules and Lennard–Jones fluid) is related to the dissipated energy at the contraction entry. The large deformation that the linear molecules experience and the evolution of the normal stress at the contraction entry follow a different trajectory in the relaxation process past the contraction, generating large hysteresis loops. The area enclosed by these cycles is related to the dissipated energy. Large shear stresses developed near the re-entrant corners as well as the vortex formation, dependent on the Deborah number, are also predicted at the exit of the contraction. To our knowledge, for the first time, the excessive pressure losses found in experimental contraction flows can be explained theoretically.     

A comparative study of crack propagation models for PMMA and PVC

An analysis of examining the validity of a unified approach proposed earlier by the authors for the fatigue crack propagation (FCP) of engineering materials to include PMMA and PVC is described. The proposed formulation has been shown capable of characterizing a diversified range of materials with a master FCP diagram and expressed as da/dN = A(ΔG)^m/(G_c − G_max).An experimental program is undertaken to measure fatigue growth rate with the standard compact tension specimen. The FCP results are for the first instance analysed for each material using the unified formulation. The validity of the formulation for producing a master FCP diagram is verified when the fatigue crack growth rates of the materials are successfully characterized in one master diagram, yielding an excellent coefficient of correlation of 0.993. No such success is attained using a number of conventional FCP laws considered most acceptable to characterize polymeric materials.