Nanoindentation (nanometer scale, extremely small) and impact (microsecond scale, extremely fast) experiments are two important techniques for characterizing modern material systems. However, these two experiments were often studied individually. In this pilot study, a multiscale indentation mechanics approach is proposed to correlate these two very different mechanics events acting on the same target materials using a spherical indenter and a projectile. The contact stiffness of nanoindentation of a target material is fitted using Hertz’s contact law, and then the contact stiffness of impact is obtained using a simplified multiscale relation. Therefore, the maximum impact force of a projectile impact can be predicted by inputting the impact energy and the contact stiffness of impact. The above new approach was validated by drop-weight impact experiments of polymers and structural composite materials subjected to low-energy impact. Results show that only a few minutes are needed to predict the maximum impact force.
DanielIMIshaiO. Engineering mechanics of composite materials. New York, NY: Oxford University Press, 2005.
2.
YangSHSunCT. Indentation law for composite laminates. ASTM STP1982; 787(1): 425–449.
3.
GeubellePHBaylorJS. Impact-induced delamination of composites: a 2D simulation. Composites B: Eng1998; 29(5): 589–602.
4.
LiGPangSSHelmsJE, et al.Low velocity impact response of GFRP laminates subjected to cycling moistures. Polym Compos2000; 21(5): 686–695.
5.
XuLRKrishnanANingH, et al.A seawater tank approach to evaluate the dynamic failure and durability of E-glass/vinyl ester marine composites. Comp Part B: Eng2012; 43(5): 2480–2486.
6.
GuanZHeWChenJ, et al.Permanent indentation and damage creation of laminates with different composite systems: an experimental investigation. Polym Compos2014; 35(5): 872–883.
7.
ZhangJZhaoLLiM, et al.Compressive fatigue behavior of low velocity impacted and quasi-static indented CFRP laminates. Compos Structures2015; 133: 1009–1015.
8.
GuGXTakaffoliMHsiehAJ, et al.Biomimetic additive manufactured polymer composites for improved impact resistance. Extreme Mech Lett2016; 9: 317–323.
9.
ChenYHouSFuK, et al.Low-velocity impact response of composite sandwich structures: modelling and experiment. Compos Structures2017; 168: 322–334.
10.
MiaoCTippurHV. Measurement of sub-micron deformations and stresses at microsecond intervals in laterally impacted composite plates using digital gradient sensing. J Dynamic Behavior Mater. 2018; 4(3): 336–358.
11.
ThorssonSIWaasAMRassaianM. Low-velocity impact predictions of composite laminates using a continuum shell based modeling approach part A: Impact study. Int J Sol Struc2018; 155: 185–200.
12.
KedirNKirkCDGuoZ, et al.Real-time visualization of impact damage in monolithic silicon carbide and fibrous silicon carbide ceramic composite. Int J Impact Eng2019; 129: 168–179.
13.
ZhaiXGaoJLiaoH, et al.Mechanical behaviors of auxetic polyurethane foam at quasi-static, intermediate and high strain rates. Int J Impact Eng2019; 129: 112–118.
14.
LinSThorssonSIWaasAM. Predicting the low velocity impact damage of a quasi-isotropic laminate using EST. Compos Structures2020; 251: 112530.
15.
ZhangDZhengXZhouJ, et al.Bridging the low-velocity impact energy versus impact damage and residual compression strength for composite laminates. J Reinforced Plastics Compos2021; 40(9–10): 378–390.
16.
SunCTChattopadhyayS. Dynamic response of anisotropic laminated plates under initial stress to impact of a mass. J Appl Mech1975; 42(3): 693–698.
17.
SankarBV. Scaling of low-velocity impact for symmetric composite laminates. J Reinforced Plastics Composites1992; 11(3): 296–309.
18.
AbrateS.Impact on composite structures. New York, NY: Cambridge University Press, 1998.
19.
XuLRRosakisAJ. Impact failure characteristics in sandwich structures: part I: basic failure mode selection. Int J Sol Struc2002; 39(16): 4215–4235.
20.
XuLRRosakisAJ. Impact damage visualization of heterogeneous two-layer materials subjected to low-speed impact. Int J Damage Mech2005; 14(3): 215–233.
21.
OliverWCPharrGM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res1992; 7(6): 1564–1583.
22.
ChenXVlassakJJ. Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J Mater Res2001; 16(10): 2974–2982.
23.
MulianaAHaj-AliRMStewardR, et al.Artificial neural network and finite element modeling of nanoindentation tests. Metall Mat Trans A2002; 33(7): 1939–1947.
24.
GregoryJRSpearingSM. Nanoindentation of neat and in situ polymers in polymer–matrix composites. Composites Science Technology2005; 65(3–4): 595–607.
25.
NakamuraTGuY. Identification of elastic–plastic anisotropic parameters using instrumented indentation and inverse analysis. Mech Materials2007; 39(4): 340–356.
26.
PoonBRittelDRavichandranG. An analysis of nanoindentation in linearly elastic solids. Int J Sol Struct2008; 45(24): 6018–6033.
27.
HeinrichCWaasAMWinemanAS. Determination of material properties using nanoindentation and multiple indenter tips. Int J Sol Struct2009; 46(2): 364–376.
28.
CaoGChenXXuZH, et al.Measuring mechanical properties of micro-and nano-fibers embedded in an elastic substrate: theoretical framework and experiment. Compos Part B: Eng2010; 41(1): 33–41.
29.
GaoYFLarsonBCLeeJH, et al.Lattice rotation patterns and strain gradient effects in face-centered-cubic single crystals under spherical indentation. J Appl Mech2015; 82(6): 1007–1016.
30.
VasconcelosLSDXuRLiJ, et al.Grid indentation analysis of mechanical properties of composite electrodes in Li-ion batteries. Extreme Mech Lett2016; 9: 495–502.
31.
DuYXuTShawTM, et al.A novel tri-layer nanoindentation method to measure the mechanical properties of a porous brittle ultra-low-k dielectric thin film. Extreme Mech Lett2017; 13: 100–107.
32.
Fisher-CrippsAC. Nanoindentation. New York NY: Springer, 2011.
XuLRMartinezRZhaoK. Measurements of through-thickness young's moduli of fibrous composite laminates using nanoindentation. J Eng Mater Tech2019; 141(3).
35.
AndrewsEWGiannakopoulosAEPlissonE, et al.Analysis of the impact of a sharp indenter. Int Journal Solids Structures2002; 39(2): 281–295.
36.
QuinnGDPatelPJLloydI. Effect of loading rate upon conventional ceramic microindentation hardness. J Res Natl Inst Stand Technol2002; 107(3): 299.
37.
MartinezRXuLR. Comparison of the Young’s moduli of polymers measured from nanoindentation and bending experiments. MRS Commun2014; 4(3): 89–93.
38.
FloresMMollenhauerDRunatungaV, et al.High-speed 3D digital image correlation of low-velocity impacts on composite plates. Composites Part B: Eng2017; 131: 153–164.
39.
YanHOskayCKrishnanA, et al.Compression-after-impact response of woven fiber-reinforced composites. Compt Sci Tech2010; 70(14): 2128–2136.
40.
RhymerJKimHRoachD. The damage resistance of quasi-isotropic carbon/epoxy composite tape laminates impacted by high velocity ice. Compos A: Appl Sci Manuf2012; 43(7): 1134–1144.
41.
BeerFPJohnstonER. Mechanics of materials. New York, NY: McGraw-Hill, 2014.
