Powerlaw creep and residual stresses in a carbopo

Authors: Pierre Lidon Louis Villa Sébastien Manneville

Publish Date: 2016/08/27

Volume: 56, Issue: 3, Pages: 307-323

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Abstract

We report on the interplay between creep and residual stresses in a carbopol microgel When a constant shear stress σ is applied below the yield stress σ y the strain is shown to increase as a power law of time γt = γ 0 + t/τ α with an exponent α = 039 ± 004 that is strongly reminiscent of Andrade creep in hard solids For applied shear stresses lower than some typical value σ c ≃ 02σ y the microgel experiences a more complex anomalous creep behavior characterized by an initial decrease of the strain that we attribute to the existence of residual stresses of the order of σ c that persist after a rest time under a zero shear rate following preshear The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects We discuss our results in light of previous works on colloidal glasses and other soft glassy systemsFlow curve shear stress σ vs shear rate dot gamma of a 1 wt carbopol microgel measured in a sandblasted coneandplate geometry by decreasing the shear rate in logrithmicallyspaced steps of 5 s each The red solid line is the best HerschelBulkley fit sigma =sigma text y+kdot gamma n with σ y = 102 Pa n = 060 and k = 33 Pas n inferred from the minimization procedure described in the text The upper left inset shows σ−σ y with σ y = 102 Pa as a function of dot gamma in logarithmic scales The upper right inset shows the residuals χ 2 of the best powerlaw fit of σ−σ y vs dot gamma when varying the value of the yield stress σ y see textStill it should be noted that we observe a reproducibility of the best HB fit parameters of only about 10 For instance for the same preparation batch we found values of σ y ranging from 95 to 105 Pa from one loading of the coneandplate geometry to the other Since the flow curves are measured through decreasing shear rate sweeps the loading history is efficiently erased at high shear rates and such variations can only be explained by small differences in the sample volume from one loading to the other We checked that the various flow curves are simply shifted along the stress axis from one measurement to the other and that the scatter is typically 1 Pa which confirms that variations in HB parameters essentially stem from variations in the loaded sample volumea Elastic modulus Gprime red and viscous modulus Gprime prime blue vs frequency f after a rest time t w = 300 s following preshear under a constant shear rate dot gamma text p=100~mathrm s1 for a duration t p = 60 s The strain amplitude is fixed to γ = 1 and the frequency is logarithmically swept down The orange solid line shows that Gprime prime sim f044 for fgtrsim 02~text Hz b Gprime red left axis Gprime prime blue left axis and stress amplitude σ black right axis vs strain amplitude γ after the same preparation protocol as in a The frequency is fixed to f = 1 Hz and the strain amplitude γ is logarithmically swept up with a duration of 16 s per point One has Gprime gamma =Gprime prime gamma for γ ∗≃200 which corresponds to σ ∗≃36 Pa The red solid line is the best linear fit σ = G 0 γ for γ 80 leading to G 0 = 34 Pa The dotted line indicates the end of the linear regime at γ ≃ 80 Creep and residual stresses in carbopol microgels with concentrations C = 06 wt blue 1 wt black and 2 wt red a Strain responses γt−γ 0 for σ ≃ 04σ y plotted in logarithmic scales together with Andrade fits yellow solid lines C σ/σ y γ 0 α = 06 wt 038 99 040 1 wt 036 89 037 2 wt 035 162 040 b Strain responses γt for σ/σ y≤01 plotted in semilogarithmic scales for C σ/σ y = 06 wt 004 1 wt 004 2 wt 01 c Residual stress σ r after a relaxation over t w = 600 s as a function of the preshear rate dot gamma text p for t p = 60 s Solid lines are power laws with exponent −02

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