An S-N curve (also known as a Wöhler curve) visualizes the relationship between alternating stress amplitude and the number of cycles to failure for a material under fatigue loading. Both axes typically use logarithmic scales, with stress on the y-axis and cycle count on the x-axis. This plot is fundamental for predicting material fatigue life and identifying key material properties such as ultimate strength, yield strength, and endurance limit.
#' anyplot.ai
#' sn-curve-basic: S-N Curve (Wöhler Curve)
#' Library: ggplot2 3.5.1 | R 4.4.1
#' Quality: 89/100 | Created: 2026-05-20
library(ggplot2)
library(dplyr)
library(scales)
library(ragg)
set.seed(42)
# Theme tokens
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
INK_MUTED <- if (THEME == "light") "#6B6A63" else "#A8A79F"
IMPRINT <- c("#009E73", "#C475FD", "#4467A3", "#BD8233",
"#AE3030", "#2ABCCD", "#954477")
GRID <- adjustcolor(INK_SOFT, alpha.f = 0.25)
# AISI 1045 Steel material properties (MPa)
sigma_u <- 750 # Ultimate tensile strength
sigma_y <- 530 # Yield strength
sigma_e <- 375 # Endurance limit (~50% × UTS, engineering standard for steel)
# Basquin equation: log10(N) = C0 - k * log10(stress)
# C0 chosen so sigma_e maps to N ≈ 10^6 (conventional steel endurance life)
k <- 10
C0 <- 31.74
# N at endurance limit — left boundary of infinite-life zone
N_endurance <- 10^(C0 - k * log10(sigma_e))
# Fatigue test specimens: multiple replicates per stress level (all above endurance limit)
stress_levels <- c(620, 580, 540, 500, 460, 430, 410, 390)
reps <- c(2, 3, 2, 3, 2, 3, 2, 3)
df <- data.frame(stress = rep(stress_levels, reps)) |>
mutate(cycles = 10^(C0 - k * log10(stress) + rnorm(n(), 0, 0.12)))
# Basquin fit line — log-spaced in cycle direction for accurate log-scale rendering
fit_df <- data.frame(
cycles = 10^seq(3, log10(N_endurance * 0.998), length.out = 300)
) |> mutate(stress = 10^((C0 - log10(cycles)) / k))
# Plot
p <- ggplot() +
# Infinite-life zone: stronger fill to emphasize key engineering insight
annotate("rect",
xmin = N_endurance, xmax = 10^8,
ymin = 310, ymax = sigma_e,
fill = IMPRINT[5], alpha = 0.14
) +
# Reference lines for key material properties
geom_hline(yintercept = sigma_u, linetype = "dashed",
color = IMPRINT[2], linewidth = 0.65, alpha = 0.85) +
geom_hline(yintercept = sigma_y, linetype = "dashed",
color = IMPRINT[3], linewidth = 0.65, alpha = 0.85) +
# Endurance limit thicker — the key design threshold for infinite life
geom_hline(yintercept = sigma_e, linetype = "longdash",
color = IMPRINT[5], linewidth = 1.1, alpha = 0.95) +
# Basquin fit curve
geom_line(data = fit_df, aes(x = cycles, y = stress),
color = INK_MUTED, linewidth = 1.0) +
# Test data scatter (multiple replicates per stress level)
geom_point(data = df, aes(x = cycles, y = stress),
shape = 21, size = 3.0, stroke = 0.5,
color = IMPRINT[1], fill = IMPRINT[1], alpha = 0.85) +
# Reference line labels — right-aligned at x = 10^7.5
annotate("text", x = 10^7.5, y = sigma_u * 1.05,
label = "Ultimate Strength (750 MPa)",
color = IMPRINT[2], hjust = 1, vjust = 0, size = 4.0) +
annotate("text", x = 10^7.5, y = sigma_y * 1.05,
label = "Yield Strength (530 MPa)",
color = IMPRINT[3], hjust = 1, vjust = 0, size = 4.0) +
annotate("text", x = 10^7.5, y = sigma_e * 1.06,
label = "Endurance Limit (375 MPa)",
color = IMPRINT[5], hjust = 1, vjust = 0, size = 4.0,
fontface = "bold") +
# Infinite-life region label inside shaded zone
annotate("text", x = 10^7.2, y = 340,
label = "Infinite Life\nRegion",
color = INK_MUTED, hjust = 0.5, size = 3.2, fontface = "italic") +
# Log-log axes
scale_x_log10(
limits = c(1e3, 10^8),
breaks = 10^(3:8),
labels = scales::trans_format("log10", scales::math_format(10^.x))
) +
scale_y_log10(
limits = c(310, 900),
breaks = c(350, 400, 500, 600, 700, 800),
labels = scales::comma_format(accuracy = 1)
) +
labs(
title = "sn-curve-basic · r · ggplot2 · anyplot.ai",
x = "Cycles to Failure",
y = "Stress Amplitude (MPa)",
caption = "Basquin model: log N = 31.7 − 10 · log σ | AISI 1045 steel"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major.x = element_blank(),
panel.grid.major.y = element_line(color = GRID, linewidth = 0.3),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(color = INK_SOFT, linewidth = 0.5),
axis.ticks = element_blank(),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = 13, face = "bold"),
plot.caption = element_text(color = INK_MUTED, size = 7, hjust = 1),
plot.margin = margin(10, 20, 10, 10, "pt")
)
# Save
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Part of S-N Curve (Wöhler Curve) on anyplot.ai.