Abstract
Rubbers reinforced with rigid particles are used in high-volume applications, including tyres, dampers, belts and hoses1. Many applications require high modulus to resist excessive deformation and high fatigue threshold to resist crack growth under cyclic load. The particles are known to greatly increase modulus but not fatigue threshold. For example, adding carbon particles to natural rubber increases its modulus by one to two orders of magnitude1,2,3, but its fatigue threshold, reinforced or not, has remained approximately 100 J m−2 for decades4,5,6,7. Here we amplify the fatigue threshold of particle-reinforced rubbers by multiscale stress deconcentration. We synthesize a rubber in which highly entangled long polymers strongly adhere with rigid particles. At a crack tip, stress deconcentrates across two length scales: first through polymers and then through particles. This rubber achieves a fatigue threshold of approximately 1,000 J m−2. Mounts and grippers made of this rubber bear high loads and resist crack growth over repeated operation. Multiscale stress deconcentration expands the space of materials properties, opening doors to curtailing polymer pollution and building high-performance soft machines.
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Data availability
The cyclic stress–stretch curves and energy release rates as a function of stretch for all synthesis conditions, as well as the Arduino code for the fatigue testers, are provided in the Supplementary Information. Raw monotonic and cyclic stress–stretch curves are available from the corresponding authors on request.
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Acknowledgements
This work was supported by the Materials Research Science and Engineering Centers (Grant DMR-2011754) and by the Air Force Office of Scientific Research (Grant FA9550-20-1-0397). J.S. was supported by a National Science Foundation Graduate Research Fellowship (Grant DGE1745303). J.K. was supported by the Kwanjeong Lee Chong Hwan Educational Foundation of Korea (Grant KEF-2017) and by the Korean Government (Electronics and Telecommunications Research Institute Grant 21YU1100). Silica nanoparticles used in this work were provided by Cabot Corporation. We acknowledge conversations on silica nanoparticles with A. Sanchez and D. Fomitchev at Cabot Corporation. We thank G. Zhang for measuring the sol and gel fractions.
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J.S. and J.K. designed the study and analysed the results. J.S. prepared samples and conducted monotonic and cyclic mechanical tests without cracks. J.K. measured crack growth and obtained images. J.S. and J.K. conducted demonstrations. Y.K. and Z.S. supervised the research. All authors wrote the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Polymerization reaction of reinforced PEA elastomers.
The molar coefficients of TDDA and Irgacure 1173 are normalized to 1 monomer of ethyl acrylate. The number of monomers between adjacent crosslinks after polymerization is estimated as 1/(2C).
Extended Data Fig. 2 Modulus is amplified by synergy of entangled polymer network and percolated particle network.
(a) Long polymer chains form a network of sparse crosslinks and dense entanglements. Some of the polymer chains interlink with particles. (b) When particles form a percolated network, high stress transmits through the stiff particle network.
Extended Data Fig. 3 Ultimate properties.
(a) Nominal strength smax, (b) stretch at rupture λmax, (c) true strength σmax, and (d) work of fracture Wf are plotted as functions of F with lines of constant C. All properties are measured at the point of rupture in the monotonic stress-stretch curves. smax increases with increasing F, but changes with C weakly. By contrast, λmax decreases with increasing F and increasing C. σmax and Wf increase with decreasing C but do not show clear trends with F.
Extended Data Fig. 4 Reinforcement ratio.
The reinforcement ratio, R = E/E0, is plotted as a function of (a) C with lines of constant F and (b) F with lines of constant C. The reinforcement ratio is not a function of C, but is a function of F. This suggests that the modulus of the composite takes the separable form E(C, F) = R(F)E0(C). The dashed line is the Guth-Gold solution.
Extended Data Fig. 5 Modulus and hysteresis ratio in cyclic stretch.
Modulus E as a function of stretch amplitude λamp for (a) C = 10−4 with various F and (b) F = 0.15 with various C. Hysteresis ratio H as a function of stretch amplitude λamp for (a) C = 10−4 with various F and (b) F = 0.15 with various C. Both properties are calculated from the stress-stretch curves in the steady state. For composites of high F, the steady-state modulus decreases with increasing λamp. This behaviour suggests that particles form a percolated network and that large stretches induce changes in the microstructure, such as partial debonding between particles and polymers, breaking polymer chains, or formation of voids in the matrix. The modulus is insensitive to C when the polymers are highly entangled, which is consistent with the scaling E = E0R.
Extended Data Fig. 6 Damage and recovery of composites.
(a) Schematic of test. Using the pure shear geometry, a composite of F = 0.45 and C = 10−4 is stretched for three sequences of N = 5,000 cycles and allowed to rest for 1 h. (b) The peak-force decays with cycles for all sequences, but more so in the first sequence. (c) The stress-stretch curves for the last cycle (N = 5,000) overlap for all sequences. (d) The stress during recovery relaxes with time at the same rate for all sequences.
Extended Data Fig. 7 Composite without covalent interlinks between polymers and particles.
(a) Stress-stretch curves measured in uniaxial tension. Stress-stretch curves in pure shear (b) for the first load cycle and (c) after N = 5,000 cycles at various stretch amplitudes λamp. (d) Energy release rate G as a function of applied stretch λamp in the steady state, fit with a quadratic function G = a1λamp2 + a2λamp + a3. C = 10−4 for all samples. F = 0.15 for samples in (b), (c), and (d).
Extended Data Fig. 8 Crack growth measurement for F = 0.45 and C = 10−4.
A crack is cut with scissors and marked with an ink pen. The sample is observed after N cycles of loading at steady-state energy release rate G. The yellow line is used to align the images, and the red line tracks the crack tip. The crack does not grow when G ≤ 1,020 J m−2.
Extended Data Fig. 9 Fatigue crack growth.
Crack growth per cycle dc/dN as a function of energy release rate G for composites of (a) F = 0, (b) F = 0.15, (c) F = 0.25, and (d) F = 0.35 for various C.
Extended Data Fig. 10 Lift force of kirigami gripper.
(a) When a sheet is pulled, it buckles and grips a sphere. The sphere is lifted at a constant velocity. (b) The lift force is measured as a function of lift displacement for grippers of F = 0.45 and F = 0 at fixed C = 10−4. (c) A gripper of F = 0.45 and C = 10−4 shows a lift force-displacement curve that is nearly unchanged after 350,000 cycles.
Supplementary information
Supplementary Information
Supplementary Figs. 1–13 and legends for Videos 1–4.
Supplementary Video 1
Cyclic compression of mounts with various C and F.
Supplementary Video 2
Fatigue test of a mount with C = 10−4 and F = 0.45 for 33,000 cycles under compression.
Supplementary Video 3
Cyclic stretch of compliant grippers with C = 10−2 and C = 10−4 at fixed F = 0.45.
Supplementary Video 4
Lift force measurement of compliant grippers with F = 0 and F = 0.45 at fixed C = 10−4.
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Steck, J., Kim, J., Kutsovsky, Y. et al. Multiscale stress deconcentration amplifies fatigue resistance of rubber. Nature 624, 303–308 (2023). https://doi.org/10.1038/s41586-023-06782-2
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DOI: https://doi.org/10.1038/s41586-023-06782-2
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