Low Strain Rates Research Articles

Continuous dynamic recrystallization behaviors in a single-phase deformed Ti-55511 alloy by cellular automata model

In this study, the continuous dynamic recrystallization (CDRX) behaviors of a hot-deformed Ti-55511 alloy are investigated in β single-phase domain. CDRX is found to play a dominant role in the microstructure evolution during thermomechanical forming of the Ti-55511 alloy. In order to quantitatively and visually simulate the hot forming process, a probabilistic cellular automata (CA) method is established. This CA technology integrates the dislocation evolution model, subgrain nucleation rate model, misorientation evolution model, grain boundary (GB) migration model, and topology deformation model. The results of a systematic study of both microstructural evolution and macroscopic mechanical response at various strains, strain rates, and temperatures are presented. The average absolute relative error (AARE), correlation coefficient (R), and root-mean squared error (RMSE) values between the experimental and simulated stresses are 4.63 %, 0.9963, and 3.81 MPa, respectively. The deviation values of subgrain size range from 1.27 % to 17.25 %, when the temperatures varies from 920 to 980 °C. The predicted results well agree with the measured results, demonstrating the transition from a coarse and static recrystallized structure to a refined and continuous dynamic recrystallized structure. A low Zener-Hollomon (Z) parameter can effectively enhance the progress of CDRX. Higher temperatures and lower strain rates result in a larger volume fraction of CDRX. Quantitative analyses confirm that the incubation period for CDRX is significantly longer than that for subgrain formation, indicating a sustained transformation from the low-angle grain boundaries (LAGBs) to the high-angle grain boundaries (HAGBs) through the absorption of dislocations.

Sensitivity Differences in Testing of Polyurethane Condoms’ Lubricant Compatibility

Abstract Over-the-counter (OTC) personal lubricants (PLs) generally have less potent effects on condoms’ mechanical properties than do appropriate positive controls. Therefore, to assess the compatibility of OTC PLs with condoms, a test method must be more sensitive than those employed to capture the effect of a strong positive control. Using various percent compositions of selected common ingredients in commercial PLs, we attempted to differentiate between the sensitivities of different methods for testing lubricant effects on polyurethane (PU) condoms. After discrete applications of each composition, we studied induced stresses and stress-to-strain ratios at various strain rates, and stress reduction at a constant stretch, in PU condom coupons at 37°C. Swelling was studied at room temperature (RmT). Changes in the induced stress and stress-to-strain ratio because of low percent composition of a potent surrogate component were detectable only at low strain rates. A few low percent compositions of potent ingredients – though they induced insignificant changes in the material as detected by tensile testing and did not swell the PU material – noticeably reduced the percent stress at a constant stretch. Slower strain rates in tensile testing were necessary to detect the effects of low potency combinations, whereas stress reduction was the most efficient detector of change at a constant physiologically relevant strain. Absence of swelling and insignificant changes in tensile properties at high strain rates did not guarantee an absence of interactions. Manufacturers now have a more sensitive method for capturing the interactions of PU condoms with OTC PLs, which are generally less potent than appropriate positive controls.

Assessment of frequency and amplitude dependence on the cyclic degradation of polyurethane foams

AbstractMany energy absorption applications utilize flexible polymeric foams for their viscoelastic properties. It is desired that the material will perform consistently across repeated compression cycles. This study examines the effect of fatigue at low strain rates on the viscoelasticity of open‐cell polyurethane foam. Six polyurethanes of the same base composition with two porosities (70% and 80%) and three chemical indexes (79i, 100i, and 121i) are tested. Large deformation cyclic compression of the foams is conducted on a universal testing system (UTS). These data are then post‐processed leveraging dynamic mechanical analysis Fourier transform rheology to characterize changes in the viscoelasticity of the materials over fatigue cycles. Results show that foams can increase or decrease in stiffness up to 10% over 104 cycles. Specifically, higher chemical index, higher excitation frequency, and larger excitation amplitude correlate with a more pronounced decrease in stiffness. Damping can also change by 15% and correlates with chemical index and excitation frequency. Consequently, the findings suggest that internal foam structure and bulk material properties as well as applied loading parameters affect the viscoelastic fatigue response of flexible polymeric foams.

A study on the collaborative deformation mechanisms of continuous and discontinuous dynamic recrystallization under low strain rates for the Ti6455x alloy with a low activation energy

To reveal the collaborative dynamic recrystallization mechanisms occurring only at low strain rates, the Ti6455x titanium alloy was designed and prepared by hot deformation. The microstructure, activation energy, and the dynamic recrystallization (DRX) process under different strain rates and temperatures were investigated, with a corresponding mechanism revealed for the first time. Results show that at low strain rates of 0.01 and 0.001 s-1, as temperature from 1173 to 1223 K, the grain size decreases, jagged bumps appear at the grain boundaries and new small grains are produced. The activation energy of Ti6455x titanium alloy is 128.63 kJ/mol. Quantitative calculations revealed that the thermal deformation mechanisms depend on the dissipation efficiency factor, η. With an increasing value of η, the dynamic softening mechanism changes from dynamic reversion (DRV) to DRV and continuous dynamic recrystallization (CDRX). While with a high η value, CDRX and discontinuous dynamic recrystallization (DDRX) occur at a temperature of 1223 K, and a strain rate of 0.001 s-1. The collaborative deformation process proceeds because: low activation energy titanium alloys facilitate the rotation of sub-grain boundaries, while dislocations can easily migrate. This condition enables CDRX to occur, leading to the refinement of grains and producing jagged grain boundaries. Then, CDRX provides nucleation sites for DDRX, promoting grain boundary migration and breaking down grains. This mechanism can significantly refine the grain size and improve mechanical properties. It is shown that both the design of low activation energy alloys and controlling hot processing conditions are effective in the development of high-strength titanium alloys.

Construction of hot processing map, dynamic recrystallization critical conditions and kinetic model of AZ61 alloy

Under temperature of 300–450 °C and strain rates from 0.003 s−1 to 1 s−1 and deformation of 70 %, hot compression experiments of AZ61 magnesium alloy were carried out on Gleeble-1500 test machine, to study its thermal deformation behavior. Based on the dynamic material theory model, a three-dimensional hot working map was obtained. Based on the work hardening rate curves inflection point, the critical strain model was built. Subsequently, the dynamic recrystallization kinetics model was constructed according to critical conditions. The findings showed that at low strain rates and high temperatures, materials with larger power dissipation factors exhibit better processability, and at high strain rates and low temperatures, materials are more prone to instability with the increase of strain. Considering the connection between peak strain εp and critical strain εc, it is observed that εc precedes εp, indicating that dynamic recrystallization occurs before reaching the peak strain. Based on the kinetics model, observed the dynamic recrystallization volume fraction curves follow a “slow-fast-slow” changing trend, exhibiting an “S” shaped growth, which was agreed with the kinetics curve in classical dynamics.

Investigation on hot deformation behavior and microstructure evolution of superaustenitic stainless steel S31254 during elevated temperature compression testing

The study thoroughly investigated the hot deformation behavior and microstructure evolution of superaustenitic stainless steel S31254. Hot compression tests were conducted at temperatures ranging from 950 °C to 1200 °C and strain rates of 0.01–10 s−1. The flow behavior of S31254 is influenced by adiabatic heating, particularly at high strain rates. The critical conditions of dynamic recrystallization for various deformation conditions were calculated based on the “double differential method.” An rise in deformation temperature or a reduction in strain rate reduces critical stress. Using the Arrhenius equation and Zener-Hollomon parameter to represent the deformation parameters, a linear connection between peak stress and dynamic recrystallization critical conditions was determined. Electron backscattering diffraction and transmission electron microscopy were used to characterize the microstructure under various deformation conditions. The dynamic softening of superaustenitic stainless steel is mainly achieved through dynamic recrystallization. The recrystallized grains are driven by distorted energy to nucleate preferentially at high-angle grain boundaries and grow towards high misorientations. Discontinuous dynamic recrystallization characterized by grain boundary bowing out is the main recrystallization mechanism in S31254. However, at high temperatures and low strain rates (1200 °C, 0.01 s−1), the dynamic recrystallization process shifts from discontinuous to continuous, with subgrain coalescence serving as the nucleating mode.

Study on the influence of κ-carbide on the high temperature flow behavior of the medium-Mn lightweight steel: Modeling and characterization

Isothermal compression tests were carried out on the Fe-11Mn-10Al-0.9C medium-Mn lightweight steel in the temperature range from 800 °C to 1100 °C and strain rate range from 0.001 s−1 to 10 s−1 to investigate the influence of κ-carbide on the hot flow behavior. The true stress-true strain curves were analyzed to evaluate the role of κ-carbide on the softening phenomena during straining. It's found flow stress drops more remarkably from the peak point to the end of deformation at low temperature and low strain rate, that condition is favorable for the precipitation of κ-carbide instead of the occurrence of DRX. The activation energy of hot deformation based on the peak stress was calculated as 454.517 kJ mol−1, but this typical strain-compensated Arrhenius-type constitutive equation was found inappropriate to model the flow behavior of the present steel, especially at the low temperature regime. By comparison, a physically-based constitutive model consisting of Bergström's equation (ε<εp) and Kolmogorov-Johnson-Mehl-Avrami's equation (ε>εp) was developed and could predict the flow behavior of the steel accurately. Electron backscattered diffraction (EBSD) analysis revealed the formation of necklace structure at high strain rate and the dynamic recrystallization (DRX) proceeded more adequately with the decrease in strain rate and increase in the deformation temperature. The precipitation of κ-carbides in both austenite grain interior and boundaries (GI and GBs) were enhanced at relatively low deformation temperature (e.g., 800 °C) and greatly improved the peak stress by hindering the dislocation motion. With the increase of deformation, the GB κ-carbide gradually coarsened and induced the decomposition of deformed austenite via the eutectoid reaction (γ→α+κ) at lower strain rate (e.g., 0.001 s−1) due to the sufficient transformation time, consequently leading to the remarkable flow stress softening. The microstructure characterization result was in agreement with variations of parameters (i.e., U, Ω, ρp and nA) with different deformation condition.

Preliminary study on the dynamic deformation mechanism of CoCrFeNi high-entropy alloy and its application in the shaped charge liner

High-entropy alloys (HEAs) with a face-centered cubic structure offer numerous advantages, including high plasticity, good processability, and high-temperature resistance. They are also suitable for use as materials in shaped-charge liners, which can cause significant damage. In this study, CoCrFeNi HEAs were prepared, and their mechanical characteristics were examined. The results indicated that the alloy exhibited good plasticity and processability. After dynamic compression, the samples were analyzed using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). It was found that dislocation was the primary deformation mechanism at low strain rates. However, as the strain rate increased, the deformation mechanism shifted from dislocations to a combination of dislocations and twinning. The damage performance of the CoCrFeNi HEA was verified through a static penetration experiment using a conical charge. The results were then compared with simulation results obtained using the AUTODYN software. This study demonstrated that the CoCrFeNi HEA could form a condensed, stable-shaped charge jet, leading to efficient damage after penetrating the steel target plate. Therefore, after uniform treatment, the CoCrFeNi HEA can be utilized as a high-energy structural material to design shaped charge structures that achieve highly efficient damage.

Simhypo-sand: a simple hypoplastic model for granular materials and SPH implementation

This paper introduces a new hypoplastic model characterized by a simple and elegant formulation. It requires only 7 material parameters to depict salient mechanical behaviors of granular materials. The numerical implementation employs an explicit integration method, enhanced by a best-fit stress correction algorithm in a smoothed particle hydrodynamics code. The performance of this model in capturing soil behavior across a range of scenarios is demonstrated by conducting various numerical tests, including triaxial and simple shear at low strain rates, as well as granular collapse, rigid penetration and landslide process at high strain rates.

Dynamic deformation behavior of single phase VNbTa medium-entropy alloys

In this study, the deformation behavior of body-centered-cubic (BCC) VNbTa medium-entropy alloy (MEA) was studied under different strain rates ranging from 10−3 s−1 to 5000 s−1 using screw-driven testing machine and split Hopkinson pressure bar (SHPB), respectively. The alloy presents an outstanding synergy of strength and plasticity without any adiabatic shear bands even at a strain rate of 5000 s−1. Moreover, the yield strength of the alloy displays an obvious strain rate dependence, increasing by ∼94.4% from 842 MPa at 10−3 s−1 to 1637 MPa at 5000 s−1. The strain rate sensitivity (SRS) factor m and highest temperature rise under dynamic loading is calculated to be 0.2991 and 182 K, respectively, which means a strong strain rate hardening and thermal softening resistance. Microstructure evolution analyses demonstrate a transition of deformation mechanism from single dislocation slip controlling in low strain rate to a synergy of mechanical twinning and dislocation slip in high strain rate. Therefore, the excellent dynamic mechanical properties could be attributed to the synergistic effects of the strong strain rate hardening and thermal softening resistance, the mechanical twins, and the cell structures and microbands derived from dislocation slip controlling. In addition, the dynamic deformation behavior of VNbTa could also be described by a classical Johnson-Cook model. Combining the excellent cryogenic temperature mechanical properties (tensile strength of ∼1930 MPa and fracture elongation ∼27%), the present work further indicates that the VNbTa MEA has great potential for engineering applications under some extreme circumstances.

Compressive response of white matter in the brain at low strain rates

The low strain-rate response of brain parenchyma is critical to predicting prognosis in cases of hydrocephalus or cerebral edema, including in the prediction of brain stem herniation. Although rate-dependent responses of brain parenchyma are well known to arise from both viscoelasticity at higher strain rates, and it is not clear whether the tissue behaves as a fluid or a solid when loaded over periods of hours to days, and the extrapolation of rate sensitivity to lower strain rates is not clear. To address this, unconfined compression-isometric hold tests were performed on samples of white matter from porcine brains at strain rates ranging from 2/s to 2 × 10−6/s. Results showed that the apparent Young's modulus dropped from ∼3000 Pa to ∼160 Pa over this range following a power law, and that an equilibrium Young's modulus of ∼100 Pa was reached. Results reveal that brain parenchyma behaves as a compliant solid at low strain rates, and suggest that brain stem herniation is resisted by an elastic energy barrier.

High-Temperature Tensile Characteristics of an Al-Zn-Mg-Cu Alloy: Fracture Characteristics and a Physical Mechanism Constitutive Model.

High-temperature tensile tests were developed to explore the flow features of an Al-Zn-Mg-Cu alloy. The fracture characteristics and microstructural evolution mechanisms were thoroughly revealed. The results demonstrated that both intergranular fractures and ductile fractures occurred, which affected the hot tensile fracture mechanism. During high-temperature tensile, the second phase (Al2CuMg) at the grain boundaries (GBs) promoted the formation and accumulation of dimples. With the continual progression of high-temperature tensile, the aggregation/coarsening of dimples along GBs appear, aggravating the intergranular fracture. The coalescence and coarsen of dimples are reinforced at higher tensile temperatures or lower strain rates. Considering the impact of microstructural evolution and dimple formation/coarsening on tensile stresses, a physical mechanism constitutive (PMC) equation is herein proposed. According to the validation and analysis, the predictive results were in preferable accordance with the testing data, showing the outstanding reconfiguration capability of the PMC model for high-temperature tensile features in Al-Zn-Mg-Cu alloys.

Dynamic strain aging and negative strain rate sensitivity in coarse-grained Al0.3CoCrFeNi high entropy alloy under hot compression

This study investigates the deformation behavior of coarse-grained (CG) Al0.3CoCrFeNi alloy under hot compression, revealing notable strain rate sensitivity (SRS) and dynamic strain aging (DSA) phenomena. DSA is observed at temperatures between 1223 K and 1373 K, exclusively at lower strain rates (0.5 s−1 – 1 s−1), while higher strain rates (≥5 s−1) exhibit DSA absence. Non-compact {112} slip activation on dislocation forest structures is proposed as the driving force behind DSA. Negative SRS behavior at 1223 K is attributed to Ni–Al cluster-based solid solution strengthening. Activation energy calculations highlight lattice diffusion and partial dislocation constriction as contributors to hot deformation. Consistency is observed in the activation volume (V*) calculation, indicating dislocation forest formation (127–519 b3, b = Bureger's vector), diminishing to 22–46 b3 upon DSA initiation. The alloy displays delayed dislocation hardening/softening transition due to CG's impact on retarding dislocation accumulation. This behavior stems from a higher V* at yielding, prolonging the typical transition observed in fine-grained alloys with lower V*. The study elucidates the intricate interplay of microstructure, strain rate, and deformation mechanisms in CG Al0.3CoCrFeNi.

A review on the mechanical behaviour of microcellular and nanocellular polymeric foams: What is the effect of the cell size reduction?

Research on nanocellular foams is motivated in part by the promise of physical properties, in particular mechanical properties, that can go beyond the classical mechanical framework. However, due to the difficulty in obtaining foams of a given density but different cell sizes, determining the effect of cell size on the mechanical properties of polymer foams remains a challenge. To overcome this difficulty, studies on the mechanical behaviour of mesocellular, microcellular and nanocellular polymer foams have been compiled in this review article. After describing the different cellular structures between meso-, micro- and nanocellular foams, the mechanical properties are examined as a function of relative density and cell size. It is shown that for small strains and at low strain rates, nanocellular foams exhibit mechanical behaviour predicted by the Gibson and Ashby model. Relative density remains the first important factor to be taken into account when studying the Young’s modulus and buckling stress of nanocellular foams. The focus then shifts to fracture properties, as microcellular foams have already been shown to be far superior to more conventional foams. As studies are still scarce and different methodologies have been used, no general conclusions can be drawn. However, the fracture and impact properties could be greatly improved by this change in scale. The local confinement of molecular chains in polymeric nanocellular foams or the relaxation of the triaxial stress state in front of the crack tip could explain these observations.

Effects of strain rate and bedding on shale fracture mechanisms

Anisotropic shale is commonly distributed in nature and undergoes both dynamic compressive and tensile load in geological engineering. In this article, the coupling effects of strain rate and bedding structures on the fracture mechanisms of shale are investigated using a split Hopkinson pressure bar (SHPB) system. The tension–compression comparative study is conducted. The Brazilian disc method is modified, and a unified strain rate measurement method is established to comprehensively analyze shale’s fracture-related properties, including moduli, strength and energy dissipation. The results indicate that the energy dissipated by shale fracture is strongly related to its strength. The strain rate and bedding affect the anisotropic strength and dissipated energy by changing the crack density and crack propagation mode. At low or medium strain rates, the bedding orientation of shale determines the direction of crack propagation. However, at high strain rates, microcracks in different directions are widely activated in the shale, which increases the fracture degree and decreases the difference in fracture toughness between the shale’s matrix and bedding planes. This also leads to a decrease in anisotropy and causes the bedding planes to lose control over the direction of crack propagation. Additionally, the dynamic tensile strength of shale increases faster than the compressive one with the strain rate, leading to a reduction in the proportion of tensile failure under impact load. Based on the experimental findings, a new anisotropic damage constitutive model is developed to characterize the dynamic properties of shale. This model reflects the anisotropic damage evolution behaviors and aligns well with experimental results, offering a theoretical foundation for predicting shale’s dynamic fracture behavior. In addition to shale, the developed experimental methods and theoretical models can also be applied to the fracture analysis of other brittle transversely isotropic materials.

High-temperature tensile behavior and constitutive model in Co-free Fe40Mn20Cr20Ni20 high-entropy alloy

High-entropy alloys (HEAs) have attracted widespread attention from scholars as a new type of material employed in extreme environments. However, as a main kind of HEAs, many face-centered cubic single-phase HEAs are restricted in industrial applications due to their lower yield strength and high cost when containing expensive elements such as Co. In this study, dispersion strengthening by heat treatment was introduced in low-cost Co-free Fe40Mn20Cr20Ni20 HEA to improve its strength, and its high-temperature tensile behavior and constitutive model were studied to explore its potential application at high temperatures. It is found that when subjected to quasi-static room-temperature stretching, the heat-treated sample exhibits a yield strength of 534 MPa and a tensile plasticity of 26.8%. In addition, the tensile behavior of samples after heat treatment was investigated at high temperature (573–873 K) and low strain rate (10−3–10−1 s−1). The results suggest that the yield strength decreases with increasing temperature and decreasing strain rate. Moreover, at 873 K and 10−3 s−1, the electron backscatter diffraction system and x-ray diffraction results of the deformed sample indicate that the softening curve is driven from the recovery of materials. Finally, the flow stress was predicted using the Arrhenius equation and Artificial Neural Network model (ANN), and the two models were assessed using the average absolute relative error and coefficient of correlation (R). The results showed that the ANN had higher accuracy.

Bonding Behavior and Mechanism of Composite Interface Between Carbon Steel/Stainless Steel Laminates at Different Temperatures and Strain Rates

Compared to hot roll and explosive bonding, there are relatively few studies on warm/cold roll bonding under low temperature conditions. In this article, the warm/cold roll bonding simulation experiment is conducted to research the deformation, interface bonding rate, microstructure, element diffusion behavior, metallographic structure, and phase of carbon steel/stainless steel. The results show that the plastic deformation remains consistent below 400 °C but exhibits temperature sensitivity above 400 °C. The lower strain rate can increase the bonding rate, while insulation treatment may reduce the bonding rate. The formation of cracks is inhibited at 25 °C and 45% reduction rate due to the challenge of cracking the surface oxide film. Temperature significantly affects bonding, with improved performance observed above 600 °C. Uneven element distribution of bonding area may be related to the precipitated compounds, while insulation treatment increases the mutual diffusion ability of elements. The increase in temperature leads to an increase in pearlite, a decrease in ferrite, and decarburization occurs within the carbon steel matrix. The carbon elements diffuse from carbon steel to the surface of stainless steel. The increase in temperature increases the content of surface compounds.

Effect of Strain Rate on Mechanical Deformation Behavior in CuZr Metallic Glass.

Tensile tests were performed on Cu64Zr36 metallic glass at strain rates of 107/s, 108/s, and 109/s via classical molecular dynamics simulations to explore the underlying mechanism by which strain rate affects deformation behavior. It was found that strain rate has a great impact on the deformation behavior of metallic glass. The higher the strain rate is, the larger the yield strength. We also found that the strain rate changes the atomic structure evolution during deformation, but that the difference in the atomic structure evolution induced by different strain rates is not significant. However, the mechanical response under deformation conditions is found to be significantly different with the change in strain rate. The average von Mises strain of a system in the case of 107/s is much larger than that of 109/s. In contrast, more atoms tend to participate in deformation with increasing strain rate, indicating that the strain localization degree is more significant in cases of lower strain rates. Therefore, increasing the strain rate reduces the degree of deformation heterogeneity, leading to an increase in yield strength. Further analysis shows that the structural features of atomic clusters faded out during deformation as the strain rate increased, benefiting more homogeneous deformation behavior. Our findings provide more useful insights into the deformation mechanisms of metallic glass.

Deformation behavior and microstructure of pure Mg during hot shear-compression

In this study, the deformation behavior and microstructure evolution of pure Mg under hot shear-compression deformation conditions are investigated using the “Shear-Compression Specimen” as a model, which provides theoretical guidance for the investigation of the principles of surface defects in the hot extrusion process. The results showed low flow stress corresponded to a high temperature and a low strain rate, temperatures between 350–450 °C and strain rate at 5 s−1 are the perfect hot deformation parameters. The deformation generates a special texture that is bent by 45° along the extrusion direction, weakening the strong basal texture structure created by extrusion. The deformed microstructure is fine and uniformly distributed. In summary, the surface of the material is forced to undergo a complex shear-compression deformation during the hot extrusion process, while the core belongs to a simple uniaxial extrusion deformation. In some specific deformation conditions, the difference between these two may produce some defects.

Investigation on work hardening rate of Al-Zn-Mg-Cu alloy under solid solution process and thermomechanical coupled multi-step fast aging process

In this paper, the work hardening rate of Al-Zn-Mg-Cu alloy in the conditions of solid solution and thermo-mechanical coupled fast aging were investigated separately, and the main research content and results are as follows. Under the solid solution processes at different temperatures, the uniaxial tensile test curves of work hardening rate are relatively dispersed at a lower strain rate, and the work hardening rate increases with the increase of solution temperature. Then, as the strain rate increasing, the work hardening rate curves at each solution temperature gradually converge, until all curves intersect at a common intersection point. The above mechanism is attributed to the comprehensive effect of precipitates, solid solutions, and dynamic strain aging in the matrix. For the thermo-mechanical coupled aging, the work hardening rate has a great different with that of solid solution process. Consequently, the influence of pre-deformation on the work hardening rate were investigated, which concludes the curve shape type and the softening coefficient. The introduction of dislocation have some significant influences on the work hardening rate. Firstly, it makes the shape of work hardening rate curves change from shape 1 to shape 2. On the other hand, as the pre-deformation increasing, the variation law of softening coefficient shows an abnormal trend that is different from the ordinary law, which is due to the coordinated effect between dislocation density and dislocation induced precipitation. Furthermore, in order to reveal the internal mechanism in depth, the microstructure are observed by TEM (Transmission electron microscope). Finally, a targeted set of analytical models for work hardening rate were established, especially the mathematical explanation of the multicollinearity phenomenon of work hardening rate curves in the solid solution condition.