A Network Evolution Model for Recovery of the Mullins Effect in Filled Rubbers

2020 ◽  
Vol 12 (09) ◽  
pp. 2050108 ◽  
Author(s):  
Hao Chu ◽  
Ji Lin ◽  
Dong Lei ◽  
Jin Qian ◽  
Rui Xiao
Keyword(s):  
Theoretical Model ◽  
Network Evolution ◽  
Applied Strain ◽  
Polymer Chains ◽  
Chain Model ◽  
Mullins Effect ◽  
Maximum Strain ◽  
Cyclic Loading And Unloading ◽  
Filled Rubbers ◽  
Loading And Unloading

The stress-softening phenomenon, named as the Mullins effect, can widely occur in filled rubbers after cyclic loading and unloading conditions. The reloading curve is typically below the initial loading curve unless the applied strain exceeds the previously applied maximum strain. Experimental observations have also shown that the Mullins effect can be recovered by annealing the pre-deformed filled rubbers at a high temperature while the recovery level strongly depends on the annealing time and temperature. In this work, we develop a theoretical model to describe the recovery of the Mullins effect by incorporating the dynamic scission and recovery of polymer chains into the eight-chain model. Experiments have also been performed on two types of filled rubbers to validate the theory. The results show that the model is able to capture the main features of the experimental observations including the Mullins effect of virgin specimens and the recovery of the Mullins effect of pre-deformed specimens subjected to different annealed conditions.

scholarly journals Transversely isotropic cyclic stress-softening model for the Mullins effect

2012 ◽  
Vol 468 (2148) ◽  
pp. 4041-4057 ◽  
Author(s):  
Stephen R. Rickaby ◽  
Nigel H. Scott
Keyword(s):  
Residual Strain ◽  
Transversely Isotropic ◽  
Cyclic Stress ◽  
Elastic Response ◽  
Chain Model ◽  
Mullins Effect ◽  
Softening Function ◽  
Stress Softening ◽  
Cyclic Loading And Unloading ◽  
Isotropic Hyperelastic Material

This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive nonlinear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular, a carbon-filled rubber vulcanizate.

Adjustable buttons for ACL graft cortical fixation partially fail with cyclic loading and unloading

2018 ◽  
Vol 27 (8) ◽  
pp. 2530-2536 ◽  
Author(s):  
J. Glasbrenner ◽  
C. Domnick ◽  
M. J. Raschke ◽  
T. Willinghöfer ◽  
C. Kittl ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Acl Graft ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

scholarly journals Experimental Study of Stress-Seepage Coupling Properties of Sandstone under Different Loading Paths

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Xi Chen ◽  
Wei Wang ◽  
Yajun Cao ◽  
Qizhi Zhu ◽  
Weiya Xu ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Pore Pressure ◽  
Complex Loading ◽  
Friction Angle ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Compression Tests ◽  
Biot Coefficient ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

The study on hydromechanical coupling properties of rocks is of great importance for rock engineering. It is closely related to the stability analysis of structures in rocks under seepage condition. In this study, a series of conventional triaxial tests under drained condition and hydrostatic compression tests under drained or undrained condition on sandstones were conducted. Moreover, complex cyclic loading and unloading tests were also carried out. Based on the experimental results, the following conclusions were obtained. For conventional triaxial tests, the elastic modulus, peak strength, crack initiation stress, and expansion stress increase with increased confining pressure. Pore pressure weakened the effect of the confining pressure under drained condition, which led to a decline in rock mechanical properties. It appeared that cohesion was more sensitive to pore pressure than to the internal friction angle. For complex loading and unloading cyclic tests, in deviatoric stress loading and unloading cycles, elastic modulus increased obviously in first loading stage and increased slowly in next stages. In confining pressure loading and unloading cycles, the Biot coefficient decreased first and then increased, which indicates that damage has a great impact on the Biot coefficient.

Effects of Detwinning on the Inelasticity of AZ31B Sheets During Cyclic Loading and Unloading

2018 ◽  
Vol 10 (09) ◽  
pp. 1850095 ◽  
Author(s):  
H. Wang ◽  
D. Tang ◽  
D. Y. Li ◽  
Y. H. Peng ◽  
P. D. Wu
Keyword(s):  
Cyclic Loading ◽  
Magnesium Alloys ◽  
Plasticity Model ◽  
Inelastic Behavior ◽  
Deformation History ◽  
Cyclic Loading And Unloading ◽  
Polycrystal Plasticity ◽  
Self Consistent ◽  
Loading And Unloading ◽  
Previous Loading

Magnesium alloys exhibit significant inelastic behavior during unloading, especially when twinning and detwinning are involved. It is commonly accepted that noteworthy inelastic behavior will be observed during unloading if twinning occurs during previous loading. However, this phenomenon is not always observed for Mg sheets with strong rolled texture. Therefore, the inelasticity of AZ31B rolled sheets with different rolled textures during cyclic loading-unloading are investigated by elastic viscoplastic self-consistent polycrystal plasticity model. The incorporation of the twinning and detwinning model enables the treatment of detwinning, which plays an important role for inelastic behavior during unloading. The effects of texture, deformation history, and especially twinning and detwinning on the inelastic behaviors are carefully investigated and found to be remarkable. The simulated results are in agreement with the available experimental observations, which reveals that the inelastic behavior for strongly rolled sheets is very different than the extruded bars.

Residual Stresses and Differential Deformation of Electroplated Structures

1989 ◽  
Vol 33 ◽  
pp. 161-169
Author(s):  
G. Sheikh ◽  
I. C. Noyan
Keyword(s):  
Residual Stresses ◽  
Lattice Parameter ◽  
Stress Profile ◽  
X Ray ◽  
Residual Stress Profile ◽  
Cyclic Loading And Unloading ◽  
Nickel Substrates ◽  
Loading And Unloading

AbstractWe report the results of a recent study where nickel substrates electroplated with chromium were loaded in-situ on an x-ray diffractometer. This technique allows determination of lattice spacings in the vicinity of the interface for both the film and the substrate as a function of the applied load. We used such lattice parameter data, SEM observations of the surface and x-ray peak breadth data to study the partitioning of deformation between the film and the substrate. The data indicates progressive loss of adhesion between the film and the substrate with increasing deformation. We observe significant effect of electroplating residual stresses on the mechanical behavior of the system. The loss of adhesion between the film and the substrate coupled with the initial residual stress profile causes an apparent 'negative Poisson's ratio' for the film during initial stages of the loading. This effect disappears with cyclic loading and unloading.

scholarly journals Damage and fractal evolution trends of sandstones under constant-amplitude and tiered cyclic loading and unloading based on acoustic emission

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986102
Author(s):  
Dongxu Liang ◽  
Nong Zhang ◽  
Lixiang Xie ◽  
Guangming Zhao ◽  
Deyu Qian
Keyword(s):  
Acoustic Emission ◽  
Cyclic Loading ◽  
Damage Evolution ◽  
Damage Accumulation ◽  
Fractal Dimensions ◽  
Damage Variable ◽  
Constant Amplitude ◽  
Kaiser Effect ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

It is of significance to study the damage and destruction of rock under cyclic loading in geotechnical engineering. We determined the trends in damage evolution of sandstone under constant-amplitude and tiered cyclic loading and unloading under uniaxial compression. The results of the study show that (1) the variation of acoustic-emission events was consistent with the stress curves and 89% of all acoustic-emission events occurred during the cycling stages. The observed Kaiser effect was more notable in tiered cycling. (2) The damage variable increased sharply in the cycling stages and its increment was 0.07 higher for tiered cycling than constant-amplitude cycling. Sandstone exhibited greater damage under tiered cyclic loading and unloading. (3) Equations for the evolution of the damage variable under the two cycle modes were obtained by fitting of experimental data. (4) The fractal dimensions of the constant-amplitude cycle were larger than those of the tiered cycle. The process of damage and destruction presents a trend of reducing fractal dimension. The damage accumulation of sandstone under tiered cycling was faster than under constant-amplitude cycling. These results provide references for damage and early warning of rock under both constant-amplitude and tiered cyclic loading and unloading.

scholarly journals Analysis of Damage Evolution of Sandstone under Uniaxial Loading and Unloading Conditions Based on Resistivity Characteristics

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Guoyin Wu ◽  
Kui Wang ◽  
Mingjie Zhao ◽  
Zhichao Nie ◽  
Zhen Huang
Keyword(s):  
Stress State ◽  
Damage Evolution ◽  
Damage Model ◽  
Damage Variable ◽  
Uniaxial Loading ◽  
Experimental Comparison ◽  
Variable Expression ◽  
Cyclic Loading And Unloading ◽  
Sandstone Rock ◽  
Loading And Unloading

In complex rock engineering, understanding the stress state and determining stability and damage evolution are necessary. To more accurately provide a theoretical basis for judging the stress state of bedrock in engineering, this study experimentally addressed the damage evolution of sandstone under loading and unloading conditions. A theoretical relationship between rock resistivity and porosity was obtained according to the Archie formula, which allowed the derivation of the sandstone damage variable expression. Then, sandstone rock samples were used for experimental evaluation, and the feasibility of the theoretically determined damage variable was verified. Finally, through theoretical and experimental comparison analysis, we developed a correlative damage model for sandstone under uniaxial loading and unloading. The results show that the damage variable varies linearly with strain. The proposed correlative equation describes this behavior accurately for loading and unloading conditions. Based on the results of this study, the correlative damage model of sandstone under cyclic loading and unloading conditions can be further improved to be a complete constitutive damage model.

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