Technical Reference

Technical Reference Companion

Reader Edition — Advanced Glass Technology for Handheld and Industrial Devices

Joseph McFadden — McFaddenCAE.com — v8, July 2026

Scope and How to Use These Values

This companion collects the working numbers and governing relations from the audiobook series in technical format — digits, symbols, and equations rather than narration. Every value is a test-specific starting point measured under particular conditions: manufacturer datasheet values reflect the supplier's specimens, geometry, and surface condition; literature values reflect the cited environments. Nothing here is a universal constant. The intended workflow is the one the series teaches: use these values to reason, to screen, and to catch order-of-magnitude errors — then calibrate against your own parts, your own process, and your own environments before certifying anything.

Where the audio narration and this document state the same quantity, the numbers are identical; this edition simply restores digits, units, and symbolic form.

Notation

Symbol

Meaning

Symbol

Meaning

σ: Applied (far-field) tensile stress

KIC: Fracture toughness (Mode 1 critical value)

a: Crack (flaw) depth or half-length

G: Strain-energy release rate

Y: Geometry factor (≈ 1.12 for edge cracks)

γf: Fracture surface energy (per surface)

KI: Mode 1 stress-intensity factor

E, ν: Young's modulus, Poisson's ratio

Pf: Cumulative probability of failure

v, n, A: Crack velocity; stress-corrosion exponent; SCCG coefficient

σ0: Weibull characteristic strength (63.2%)

CS, DOL, CT: Surface compressive stress; depth of layer; central tension

m: Weibull modulus (scatter parameter)

rm, Am: Mirror radius; mirror constant

Governing Relations

Stress intensity at a flaw under Mode I (opening) load:

KI = Yσ √(πa)  (1)

Fast fracture criterion:

KI ≥ KIC  (2)

Energy form (Griffith/Irwin). Plane stress E′ = E; plane strain E′ = E/(1 − ν²). Critical value Gᴄ = 2γf for ideally brittle fracture:

G = KI2 / E′  (3)

Weibull cumulative probability of failure (two-parameter):

Pf(σ) = 1 − exp[ −(σ/σ0)m ]  (4)

Design strength at 90% reliability (B10):

B10 = σ0 (−ln 0.9)1/m  (5)

For m = 5, B10 ≈ 0.45 σ0; for m = 20, B10 ≈ 0.80 σ0. Datasheet mean strength (≈50% failure probability) is dangerously non-conservative as a design criterion.

Subcritical (fluid-mediated) crack growth, Region I power law:

v = da/dt = AKIn  (6)

Thermally activated form (reaction-rate control; explains climate sensitivity — rate roughly doubles per 10–15 °C within the service range):

v = v0 exp[ (−Ea + bKI) / RT ]  (7)

Time to failure under sustained stress σ, integrating Eq. 6 from initial flaw aᵢ (valid for n ≫ 2; the result is dominated by the initial stress intensity):

tf ≈ 2 KIi2−n / [ (n − 2) AY2 π σ2 ]  (8)

Fracture-surface (mirror) relation — failure stress from mirror radius; the mirror constant is composition-specific and must be calibrated:

σf √rm = Am  (9)

Interpretation discipline from the series: a large mirror alone establishes only that failure stress was low. Slow-growth conclusions require the combination — mirror size, arrest lines where present, surface and edge condition, and service history.

Table 1 — Key Material Properties

Glass

E (GPa)

K₁c / hardness

Strengthening (CS / DOL)

Notes

Corning EAGLE XG (substrate): E 73–74 GPa *** not chemically strengthened

ρ 2.38 g/cm³; strain point ≈ 669 °C; CTE ≈ 3.17 ppm/°C; display substrate (CF/TFT)

Corning Gorilla Glass Victus 2: E 79 K₁c 0.82 MPa·√m; HV 670

high CS, deep DOL (datasheet)

static bend strength 600–700 MPa; dynamic (impact) 800–1000 MPa

SCHOTT Xensation Up: E 82 GPa

CS > 900 MPa; DOL > 150 µm

ν 0.22; ρ 2.48 g/cm³; LAS composition

SCHOTT Xensation Alpha: E 80 GPa

deep-strengthened

ν 0.26; ρ 2.39 g/cm³; LABS composition; +100% drop vs. LAS on rough surfaces (maker test)

AGC Dragontrail (production ending Q3 2026): E 74 GPa. HV 673

CS > 600 MPa; DOL 35–45 µm

listed for legacy fleets and historical comparison; AGC exiting the business

Maker performance claims (e.g., drop-height survivals) are system results from specific test protocols — surface, dummy mass, and mounting all matter — not material properties.

Table 2 — Critical Strain Thresholds (screening values, quasi-static baseline)

Glass condition

Surface strain

Edge strain

Basis

Chemically strengthened aluminosilicate / LAS

0.3–0.5%

0.1–0.3%

quasi-static, ambient

Non-strengthened aluminosilicate / borosilicate

0.1–0.2%

0.05–0.1%

quasi-static, ambient

Adjustment

Factor

When applied

Dynamic (drop / impact)

+20 to +50%

strain rates ≈ 10²–10⁴ s⁻¹; subcritical growth outrun

Long-duration / environmental

−20 to −50%

sustained load or cyclic-environmental service; fluid-mediated growth active

Edge thresholds are roughly half the surface values because cutting flaws (20–100 µm) exceed surface flaws (1–10 µm) and K₁ scales with √a. A single uniform failure criterion across a glass model is non-conservative; treat edges as a distinct region. These are screening values — calibrate to your flaw population, edge finish, stressed area, rate, and environment before design use.

Table 3 — Subcritical Crack Growth Parameters (50% RH, 25 °C, soda-lime/aluminosilicate class)

Parameter

Value

Units / note

Stress corrosion exponent n

≈ 15–20

dimensionless; environment-dependent

SCCG coefficient A

10⁻⁵–10⁻⁴

m/s · (MPa·√m)⁻ⁿ

Fracture toughness K₁c

≈ 0.75 (0.70–0.85)

MPa·√m, typical cover-glass class

Region I (reaction-rate limited)

K₁ ≲ 0.25

MPa·√m; water-reaction controlled; climate-sensitive

Region II (transport-limited plateau)

K₁ ≈ 0.3–0.5

MPa·√m; water-delivery controlled

Region III (mechanically dominated)

K₁ ≳ 0.55 → K₁c

MPa·√m; environment-insensitive

Table 4 — Crack Propagation Velocity Limits and Fractographic Transitions

Quantity

Value

Note

Rayleigh wave speed, silicate glass

≈ 3000–3600 m/s

theoretical ceiling for Mode I

Terminal crack velocity (phonon / elastic-wave limited)

≈ 30–60% of Rayleigh ≈ 1500–2200 m/s

typical aluminosilicate compositions

Mirror → mist transition

≈ 0.3 × terminal velocity

onset of tip instability

Mist → hackle transition

≈ 0.5–0.6 × terminal velocity

energy shed to roughening

Bifurcation onset

> 0.6 × terminal velocity

crack branching; chaotic fracture

Table 5 — Environmental Effects on Effective Strength

Condition

Effect on strength

Mechanism

High strain rate (drop impact)

+20 to +50%

load applied faster than subcritical growth can act

−20 °C

−10 to −20%

glass-level embrittlement; note assembly effects often dominate (stiffened constraints)

+50 °C

+5 to +10%

minor viscoelastic energy dissipation

Humidity, long-term static load

−20 to −50%

fluid-mediated stress corrosion (Region I integration over time)

Aggressive cleaning (alkaline pH > 10; extended IPA)

additional −10 to −20%

accelerated subcritical growth; network attack (alkaline); oleophobic coating loss

Saline / sea-spray exposure

additional −10 to −20%

chloride-accelerated silica attack; partial surface ion-exchange reversal

Effects compound along a service history: the same part can carry a dynamic bonus during the drop and an environmental deficit accumulated before it. Temperature is a system variable — the constraint stiffness of adhesives and gaskets changes more over the service range than the glass does, redirecting how much of an event's energy arrives in the glass as tension.

Closing Note

For the reasoning behind every number in this companion — and the reasons to hold each one loosely — the four parts of the series are where the story lives. Questions and discussion are welcome: mcfadden@snet.net · McFaddenCAE.com.