ME330 Lab 1: Compression & Hardness

Load CSVs

steel_1018_data <- read.csv("M12_A_1018.csv", header = TRUE)
steel_1045_data <- read.csv("M12_A_1045.csv", header = TRUE)
al_7075_data    <- read.csv("M12_A_7075.csv", header = TRUE)
pmma_data       <- read.csv("M12_A_PMMA.csv", header = TRUE)

Extract data and Geometry

# Steel 1018
dis_1018 <- as.numeric(steel_1018_data$Displacement)
F_1018   <- as.numeric(steel_1018_data$Force)
eps_1018 <- as.numeric(steel_1018_data$Composite.strain)
l_1018 <- 64.92; d_1018 <- 19.05; A_1018 <- pi/4 * d_1018^2
sigma_eng_1018 <- F_1018 / A_1018 * 1000
sigma_true_1018 <- sigma_eng_1018 * (1 + eps_1018)
eps_true_1018 <- log(1 + eps_1018)
ultimate_1018<- max(sigma_eng_1018, na.rm = TRUE)
fracture_1018 <- length(sigma_eng_1018)

# Steel 1045
dis_1045 <- as.numeric(steel_1045_data$Displacement)
F_1045   <- as.numeric(steel_1045_data$Force)
eps_1045 <- as.numeric(steel_1045_data$Composite.strain)
l_1045 <- 39.8;  d_1045 <- 12.55; A_1045 <- pi/4 * d_1045^2
sigma_eng_1045 <- F_1045 / A_1045 * 1000
sigma_true_1045 <- sigma_eng_1045 * (1 + eps_1045)
eps_true_1045 <- log(1 + eps_1045)
ultimate_1045<- max(sigma_eng_1045, na.rm = TRUE)
fracture_1045 <- length(sigma_eng_1045)


# Aluminum 7075
dis_7075 <- as.numeric(al_7075_data$Displacement)
F_7075   <- as.numeric(al_7075_data$Force)
eps_7075 <- as.numeric(al_7075_data$Composite.strain)
l_7075 <- 39.93; d_7075 <- 12.84; A_7075 <- pi/4 * d_7075^2
sigma_eng_7075 <- F_7075 / A_7075 * 1000
sigma_true_7075 <- sigma_eng_7075 * (1 + eps_7075)
eps_true_7075 <- log(1 + eps_7075)
ultimate_7075 <- max(sigma_eng_7075, na.rm = TRUE)
fracture_7075 <- length(sigma_eng_7075)

# Plastic PMMA
dis_PMMA <- as.numeric(pmma_data$Displacement)
F_PMMA   <- as.numeric(pmma_data$Force)
eps_PMMA <- as.numeric(pmma_data$Compressive.strain)
l_PMMA <- 65.02; d_PMMA <- 19.01; A_PMMA <- pi/4 * d_PMMA^2
sigma_eng_PMMA <- F_PMMA / A_PMMA * 1000
sigma_true_PMMA <- sigma_eng_PMMA * (1 + eps_PMMA)
eps_true_PMMA <- log(1 + eps_PMMA)
fracture_PMMA <- length(sigma_eng_PMMA)
ultimate_PMMA <- max(sigma_eng_PMMA, na.rm = TRUE)

Plot All Engineering Curves in one graph

colors <- c("firebrick", "darkorange", "steelblue", "black")
labels <- c("1045 Steel", "7075 Aluminum", "1018 Steel", "PMMA")
xmax <- max(c(eps_1045, eps_7075, eps_1018, eps_PMMA), na.rm = TRUE)
ymax <- max(c(sigma_eng_1045, sigma_eng_7075, sigma_eng_1018, sigma_eng_PMMA), na.rm = TRUE)
par(mfrow = c(1, 1))
plot(eps_1045, sigma_eng_1045, type = "l", col = colors[1], lwd = 2,
     xlim = c(0, xmax), ylim = c(0, ymax),
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "Stress vs. Strain Curves (All Materials)")
lines(eps_7075, sigma_eng_7075, col = colors[2], lwd = 2)

lines(eps_1018, sigma_eng_1018, col = colors[3], lwd = 2)
lines(eps_PMMA, sigma_eng_PMMA, col = colors[4], lwd = 2)

legend("topright", legend = labels, col = colors, lwd = 2, bty = "n")
grid()

Aluminum 7075 Engineering vs. True

plot(eps_7075, sigma_eng_7075, type = "n",
     xlab = "Strain (mm/mm)", ylab = "Stress (MPa)",
     main = "7075 Aluminum: Engineering vs True")
grid()

points(eps_7075, sigma_eng_7075, col = "royalblue", pch = 16)
points(eps_true_7075, sigma_true_7075, col = "darkorange", pch = 16)

legend("bottomright",
       legend = c("Engineering σ–ε", "True σ–ε"),
       col = c("royalblue", "darkorange"),
       pch = 16, bty = "n")

Four Material Stress-Strain Curve Comparsion

par(mfrow = c(2, 2)) 
# 1045 Steel
plot(eps_1045, eng_stress_1045,
     type = "l", col = "firebrick", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "1045 Steel")
points(eps_1045, eng_stress_1045, col = "firebrick", pch = 16)

points(eps_1045[ultimate_1045], eng_stress_1045[ultimate_1045], col = "purple", pch = 17, cex = 1.5)
legend("bottomright", legend = c("Ultimate Stress"), pch = 17, col = "purple", bty = "n")

grid()

# 7075 Aluminum
plot(eps_7075, eng_stress_7075,
     type = "l", col = "darkorange", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "7075 Aluminum")

points(eps_7075, eng_stress_7075, col = "darkorange", pch = 16)
points(eps_7075[ultimate_7075], eng_stress_7075[ultimate_7075], col = "purple", pch = 17, cex = 1.5)

legend("bottomright", legend = c("Ultimate Stress"), pch = 17, col = "purple", bty = "n")
grid()

# 1018 Steel
plot(eps_1018, eng_stress_1018,
     type = "l", col = "steelblue", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "1018 Steel")
points(eps_1018, eng_stress_1018, col = "steelblue", pch = 16)

points(eps_1018[ultimate_1018], eng_stress_1018[ultimate_1018], col = "purple", pch = 17, cex = 1.5)
legend("bottomright", legend = c("Ultimate Stress"), pch = 17, col = "purple", bty = "n")

grid()

# PMMA
plot(eps_PMMA, eng_stress_PMMA,
     type = "l", col = "black", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "PMMA")

points(eps_PMMA, eng_stress_PMMA, col = "black", pch = 10)
points(eps_PMMA[ultimate_PMMA], eng_stress_PMMA[ultimate_PMMA], col = "purple", pch = 17, cex = 1.5)

legend("bottomright", legend = c("Ultimate Stress"), pch = 17, col = "purple", bty = "n")
grid()

# Eye-balling ultimate stress (will adjust based on the best fit line)
eps_yield_1045 = 0.0033
eps_yield_7075 = 0.004
eps_yield_1018 = 0.0026
eps_yield_PMMA = 0.07

E_1045  <- coef(lm(eng_stress_1045[eps_1045 <= eps_yield_1045] ~ 0 + eps_1045[eps_1045 <= eps_yield_1045]))[1]
E_7075  <- coef(lm(eng_stress_7075[eps_7075 <= eps_yield_7075] ~ 0 + eps_7075[eps_7075 <= eps_yield_7075]))[1]
E_1018  <- coef(lm(eng_stress_1018[eps_1018 <= eps_yield_1018] ~ 0 + eps_1018[eps_1018 <= eps_yield_1018]))[1]
E_PMMA  <- coef(lm(eng_stress_PMMA[eps_PMMA <= eps_yield_PMMA] ~ 0 + eps_PMMA[eps_PMMA <= eps_yield_PMMA]))[1]

cat("E_1045  =", E_1045, "MPa\n")

E_1045  = 195069.4 MPa

cat("E_7075  =", E_7075, "MPa\n")

E_7075  = 71655.21 MPa

cat("E_1018  =", E_1018, "MPa\n")

E_1018  = 104377.6 MPa

cat("E_PMMA  =", E_PMMA, "MPa\n")

E_PMMA  = 1958.495 MPa

1045 Steel

# --- 1045 Steel ---
E_1045 <- coef(fit_1045)[1]
sigma_offset_1045 <- E_1045 * (eps_1045 - 0.002)
diff_1045 <- eng_stress_1045 - sigma_offset_1045
i_1045 <- which(diff(sign(diff_1045)) != 0)[1]
yield_stress_1045 <- eng_stress_1045[i_1045]
yield_strain_1045 <- eps_1045[i_1045]

plot(eps_1045, eng_stress_1045,
     type = "l", col = "firebrick", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "1045 Steel")
points(eps_1045, eng_stress_1045, col = "firebrick", pch = 16)

abline(a = 0, b = coef(fit_1045), col = "purple", lwd = 2, lty = 2)
abline(a = -coef(fit_1045) * 0.002, b = coef(fit_1045), col = "darkgreen", lwd = 2, lty = 3)

points(yield_strain_1045, yield_stress_1045, pch = 19, col = "red")
text(x = yield_strain_1045,
     y = yield_stress_1045,
     labels = paste0(round(yield_stress_1045, 1), " MPa"),
     pos = 3, col = "red", cex = 1.5)

cat("\n--- 1045 Steel ---\n")

--- 1045 Steel ---

cat("E =", round(E_1045, 2), "MPa\n")

E = 195069.4 MPa

cat("0.2% Offset Yield Strain =", round(yield_strain_1045, 5), "\n")

0.2% Offset Yield Strain = 0.00405 

cat("0.2% Offset Yield Stress =", round(yield_stress_1045, 2), "MPa\n")

0.2% Offset Yield Stress = 452.54 MPa

7075 Aluminium

# --- 0.2% Offset Yield Calculation ---
E_7075 <- coef(fit_7075)[1]
sigma_offset_7075 <- E_7075 * (eps_7075 - 0.002)
diff_7075 <- eng_stress_7075 - sigma_offset_7075
i_7075 <- which(diff(sign(diff_7075)) != 0)[1]
yield_stress_7075 <- eng_stress_7075[i_7075]
yield_strain_7075 <- eps_7075[i_7075]

# --- Plot ---
plot(eps_7075, eng_stress_7075,
     type = "l", col = "darkorange", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "7075 Aluminum")
points(eps_7075, eng_stress_7075, col = "darkorange", pch = 16)

# Elastic best-fit and offset lines
fit_7075 <- lm(eng_stress_7075[eps_7075 <= eps_yield_7075] ~ 0 + eps_7075[eps_7075 <= eps_yield_7075])
abline(a = 0, b = coef(fit_7075), col = "purple", lwd = 2, lty = 2)
abline(a = -coef(fit_7075) * 0.002, b = coef(fit_7075), col = "darkgreen", lwd = 2, lty = 3)

# Yield point marker
points(yield_strain_7075, yield_stress_7075, pch = 19, col = "red")

# Annotate yield point
text(x = yield_strain_7075,
     y = yield_stress_7075,
     labels = paste0(round(yield_stress_7075, 1), " MPa"),
     pos = 3, col = "red", cex = 1.5)

cat("\n--- 7075 Aluminum ---\n")

--- 7075 Aluminum ---

cat("E =", round(E_7075, 2), "MPa\n")

E = 71655.21 MPa

cat("0.2% Offset Yield Strain =", round(yield_strain_7075, 5), "\n")

0.2% Offset Yield Strain = 0.00551 

cat("0.2% Offset Yield Stress =", round(yield_stress_7075, 2), "MPa\n")

0.2% Offset Yield Stress = 270.38 MPa

1018 Steel

# --- 0.2% Offset Yield Calculation ---
E_1018 <- coef(fit_1018)[1]
sigma_offset_1018 <- E_1018 * (eps_1018 - 0.002)
diff_1018 <- eng_stress_1018 - sigma_offset_1018
i_1018 <- which(diff(sign(diff_1018)) != 0)[1]
yield_stress_1018 <- eng_stress_1018[i_1018]
yield_strain_1018 <- eps_1018[i_1018]

# --- Plot ---
plot(eps_1018, eng_stress_1018,
     type = "l", col = "steelblue", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "1018 Steel",
     xlim = c(0, 0.005),       # expand x-axis a bit
     ylim = c(0, 310))         # expand y-axis to make space for red text

points(eps_1018, eng_stress_1018, col = "steelblue", pch = 16)

# Elastic best-fit and offset lines
fit_1018 <- lm(eng_stress_1018[eps_1018 <= eps_yield_1018] ~ 0 + eps_1018[eps_1018 <= eps_yield_1018])
abline(a = 0, b = coef(fit_1018), col = "purple", lwd = 2, lty = 2)
abline(a = -coef(fit_1018) * 0.002, b = coef(fit_1018), col = "darkgreen", lwd = 2, lty = 3)

# Yield point marker
points(yield_strain_1018, yield_stress_1018, pch = 19, col = "red")

# Annotate yield point
text(x = yield_strain_1018,
     y = yield_stress_1018,
     labels = paste0(round(yield_stress_1018, 1), " MPa"),
     pos = 3, col = "red", cex = 2)

cat("\n--- 1018 Steel ---\n")

--- 1018 Steel ---

cat("E =", round(E_1018, 2), "MPa\n")

E = 104377.6 MPa

cat("0.2% Offset Yield Strain =", round(yield_strain_1018, 5), "\n")

0.2% Offset Yield Strain = 0.00445 

cat("0.2% Offset Yield Stress =", round(yield_stress_1018, 2), "MPa\n")

0.2% Offset Yield Stress = 272.79 MPa

EMMA Plastic

# --- 0.2% Offset Yield Calculation ---
E_PMMA <- coef(fit_PMMA)[1]
sigma_offset_PMMA <- E_PMMA * (eps_PMMA - 0.002)
diff_PMMA <- eng_stress_PMMA - sigma_offset_PMMA
i_PMMA <- which(diff(sign(diff_PMMA)) != 0)[1]
yield_stress_PMMA <- eng_stress_PMMA[i_PMMA]
yield_strain_PMMA <- eps_PMMA[i_PMMA]

# --- Plot  ---
plot(eps_PMMA, eng_stress_PMMA,
     type = "l", col = "black", lwd = 2,
     xlab = "Strain (-)", ylab = "Stress (MPa)",
     main = "PMMA (Compressive Test)")
points(eps_PMMA, eng_stress_PMMA, col = "black", pch = 10)

# Elastic best-fit and offset lines
fit_PMMA <- lm(eng_stress_PMMA[eps_PMMA <= eps_yield_PMMA] ~ 0 + eps_PMMA[eps_PMMA <= eps_yield_PMMA])
abline(a = 0, b = coef(fit_PMMA), col = "purple", lwd = 2, lty = 2)
abline(a = -coef(fit_PMMA) * 0.002, b = coef(fit_PMMA), col = "darkgreen", lwd = 2, lty = 3)

# Yield point marker
points(yield_strain_PMMA, yield_stress_PMMA, pch = 19, col = "red")

# Annotate yield point with stress label
text(x = yield_strain_PMMA,
     y = yield_stress_PMMA,
     labels = paste0(round(yield_stress_PMMA, 1), " MPa"),
     pos = 3, col = "red", cex = 1.5)

cat("\n--- PMMA ---\n")

--- PMMA ---

cat("E =", round(E_PMMA, 2), "MPa\n")

E = 1958.5 MPa

cat("0.2% Offset Yield Strain =", round(yield_strain_PMMA, 5), "\n")

0.2% Offset Yield Strain = 0.05505 

cat("0.2% Offset Yield Stress =", round(yield_stress_PMMA, 2), "MPa\n")

0.2% Offset Yield Stress = 104.36 MPa

# Load package
library(knitr)



# Use your stored variables
youngs_modulus <- c(E_1018, E_1045, E_7075, E_PMMA)
yield_stress_0p2 <- c(yield_stress_1018, yield_stress_1045, yield_stress_7075, yield_stress_PMMA)
ultimate_strength <- c(ultimate_1018, ultimate_1045, ultimate_7075, ultimate_PMMA)

# Build data frame
table_data <- data.frame(
  row.names = c("Young’s Modulus", "0.2% Offset Yield Stress", "Ultimate Strength"),
  `1018 Steel` = round(c(youngs_modulus[1], yield_stress_0p2[1], ultimate_strength[1]), 2),
  `1045 Steel` = round(c(youngs_modulus[2], yield_stress_0p2[2], ultimate_strength[2]), 2),
  `7075 Aluminum Alloy` = round(c(youngs_modulus[3], yield_stress_0p2[3], ultimate_strength[3]), 2),
  `PMMA` = round(c(youngs_modulus[4], yield_stress_0p2[4], ultimate_strength[4]), 2)
)

# Print the table
kable(table_data, caption = "Table 4. Young’s Modulus, 0.2% Offset Yield Stress, and Ultimate Strength of Listed Materials")

Table 4. Young’s Modulus, 0.2% Offset Yield Stress, and Ultimate Strength of Listed Materials

	X1018.Steel	X1045.Steel	X7075.Aluminum.Alloy	PMMA
Young’s Modulus	104377.61	195069.43	71655.21	1958.50
0.2% Offset Yield Stress	272.79	452.54	270.38	104.36
Ultimate Strength	274.78	586.81	424.68	114.33

# Message
cat("Table generated successfully!\n")

Table generated successfully!