Chapter 10:Modeling of Stiffness,Strength,and Structure 473 Start Performed laboratory experiments to determine Young's modulus E)and strength ( Estimate particle normal contact stiffness (k)and normal strength(s) using Equations 3 and 4.Assume particle frictional coefficient. Estimate shear components of micro-mechanical parameters assuming k=k/2 and ss=Sa Perform numerical simulation in PFC3D No Adjust ka,k,Sn,Ss and Does numerical simulation other properties. mimic the experiment? Yes Estimation of micro-mechanical properties is completed End Fig.10.9.Flowchart of the simulation process in PFCD prepared following the procedures described in [8].Compression experi- ments were conducted under different temperature conditions to study their corresponding effects on the measured properties.Cylindrical specimens consistent with ASTM D695-02a standard were used in an MTS machine equipped with a 55,000 lb load cell.Five replicate samples were tested. A typical experimental setup is shown in Fig.10.10.Separate sets of samples were loaded at strain rates of 0.0035,0.035,and 0.35 s to investigate strain rate effects in x-aerogel
Fig. 10.9. Flowchart of the simulation process in PFC3D prepared following the procedures described in [8]. Compression experiments were conducted under different temperature conditions to study their corresponding effects on the measured properties. Cylindrical specimens Chapter 10: Modeling of Stiffness, Strength, and Structure consistent with ASTM D695-02a standard were used in an MTS machine equipped with a 55,000 lb load cell. Five replicate samples were tested. A typical experimental setup is shown in Fig. 10.10. Separate sets of samples were loaded at strain rates of 0.0035, 0.035, and 0.35 s−1 to investigate strain rate effects in x-aerogel. 473
474 S.Roy and A.Hossain Fig.10.10.Uniaxial compression testing of crosslinked silica aerogel Figure 10.11 represents the average stress-strain response for cross- linked silica aerogel specimens under compressive loading at room temp- erature at a strain rate of 0.0035s.Data for compressive yield strength, compressive stress at ultimate failure,and Young's modulus for individual sample calculated at room temperature,as well as the average values with their standard deviations,are summarized in Table 10.1.The ultimate com- pressive strength with other properties of native (uncrosslinked)silica aerogel is given in Table 10.2 for comparison. During the compression test,crosslinked aerogels were found to behave as linearly elastic under small strains(<4%)and then exhibited yield (until ~40%compressive strain),followed by densification and inelastic hardening.Aerogel samples ultimately failed at approximately 77%compressive strain,yielding an ultimate compressive strength of 186+22 MPa.The average yield stress defined at the beginning of den- sification was 4.26+0.25 MPa and occurred at approximately 4%strain
Fig. 10.10. Uniaxial compression testing of crosslinked silica aerogel Figure 10.11 represents the average stress–strain response for crosslinked silica aerogel specimens under compressive loading at room temperature at a strain rate of 0.0035 s−1 . Data for compressive yield strength, compressive stress at ultimate failure, and Young’s modulus for individual sample calculated at room temperature, as well as the average values with their standard deviations, are summarized in Table 10.1. The ultimate compressive strength with other properties of native (uncrosslinked) silica aerogel is given in Table 10.2 for comparison. During the compression test, crosslinked aerogels were found to behave as linearly elastic under small strains (<4%) and then exhibited yield (until ∼40% compressive strain), followed by densification and inelastic hardening. Aerogel samples ultimately failed at approximately 77% compressive strain, yielding an ultimate compressive strength of 186 ± 22 MPa. The average yield stress defined at the beginning of densification was 4.26 ± 0.25 MPa and occurred at approximately 4% strain. 474 S. Roy and A. Hossain