# Presentation: 378310

## Stress/Life Cyclic Fatigue Behavior of Human Dentin 		# 2684 

V. Imbeni1, R. K. Nalla1, J. H. Kinney2, M. Staninec2, S. J. Marshall2, and R. O. Ritchie1
1Materials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Materials Science and Engineering, University of California, Berkeley CA 94720
2Department of Preventive and Restorative Dental SciencesUniversity of California, San Francisco CA 9494143-0758

**Objective**

**Stress/Life Cyclic Fatigue Behavior of Human Dentin ****	****	****# 2684**
**V. Imbeni****1****, R. K. Nalla****1****, J. H. Kinney****2****, M. Staninec****2****, S. J. Marshall****2****, and R. O. Ritchie****1**
**1****Materials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Materials Science and Engineering, University of California, Berkeley CA 94720**
**2****Department of Preventive and Restorative Dental SciencesUniversity of California, San Francisco CA 9494143-0758**

** **

**Microstructure of Dentin**

**Results**

- .

**Exposed root surfaces in teeth often exhibit non-carious notches in the dentin just below the enamel-cementum junction.T****he anterior teeth are more susceptible to fracture in the gingiva, severing the crown of the tooth. ****Although such fractures have not been studied extensively, it is generally believed that tooth failure is associated either with catastrophic events induced by very high occlusal  stresses or, more plausibly, by cyclic fatigue-induced subcritical crack growth. **

**The effect of prolonged fatigue cycling on human dentin was studied ****in Hank’s Balanced Salt Solution (ambient temperature) at cyclic frequencies of  2 and 20 Hz****. The response of dentin to fatigue loading was investigated in terms of both classical (S-N/stress-life) and fracture-mechanics based approaches.** **A framework for a fracture-mechanics based life-prediction methodology for the fatigue life of teeth was developed.**

**Experimental set-up**

**Materials**

**Why?**

**Overview of typical fracture surface. The arrows indicate the probable initiation sites for the fatigue crack(s)**

**Low- and high-magnification SEM micrographs of the cyclic fatigue region of the fracture surface. Some evidence of pullout of the peritubular dentin cuffs is indicated by arrows.  **

**Low- and high-magnification SEM micrographs of the overload (fast) fracture region. Although this fracture surface looks slightly “rougher” it is essentially identical to that obtained by cyclic fatigue, at a macroscopic size-scale. Some evidence of pullout of the peritubular dentin cuffs is indicated by arrows).**

- Stress-Life data obtained at 2 Hz and 20 Hz, with the stress amplitude, **a as a function of the number of fatigue cycles to failure, *N*f.  The inset shows a typical fatigue cycle.  In the present study, a load ratio, *R* of 0.1 was used, i.e. **min*/***max = 0.1.

- Typical stiffness loss during a Stress-Life test. Most of the stiffness loss occurs late in the lifetime of the specimen.  This stiffness loss is assumed to be the result of the propagation of a through-thickness fatigue crack for the purpose of obtaining fatigue crack growth data.

- Fatigue crack growth data is shown with the stress-intensity range, *K* as a function of the crack growth rate, d*a*/d*N*.  A linear fit for the data presented is also shown.  The inset shows an illustration of the geometrical configuration used for these calculations.

**S/N**
**approach**

**Damage tolerant**
** ****approach**

**DISCUSSION&CONCLUSIONS**
-  **“****Smooth-bar” stress-life (*****S/N*****) behavior for dentin was observed to be “metal-like” with decreasing fatigue lives associated with increasing stress amplitude.  *****S/N***** curves (at a load ratio of *****R***** = 0.1) displayed an apparent fatigue limit at 10****6****-10****7**** cycles, which was estimated to be ~25 and 45 MPa, i.e., ~15 to 30% of the tensile strength, for cyclic frequencies of 2 and 20 Hz, respectively. **
** ****Akin to many brittle materials, the morphology of the fracture surfaces created during fatigue-crack propagation were essentially identical to those created during overload (catastrophic) failure**
**Using a stiffness-loss technique, fatigue-crack growth rates for human dentin were determined from the *****S*****/*****N***** results and related to the stress-intensity range.  Resulting d*****a*****/d*****N***** vs. *********K***** plots suggested a simple Paris power-law relationship, d*****a*****/d*****N ********* *********K******m*****, with *****m***** ~ 17. Extrapolation to ~10****-10**** m/cycle yielded an estimate of the fatigue threshold of *********K*****TH**** ~ ***** *****1.04 MPa********m, i.e., ~60% of the fracture toughness, *****K*****c****, of dentin.**** **
** ****It should be noted here that this simple fracture mechanics analysis is presented merely as an illustration of how life prediction could be performed for human teeth.  We believe that this approach is inherently more reliable than the traditional stress-life approach, which would not have predicted any failures for the physiological stresses of 20 MPa. Because of  uncertainties in the precise loading and crack size/shape configurations, these predictions must only be considered as a rough indication of the life of the tooth.  However, they do indicate the general trend that for typical physiological stresses of 5 to 20 MPa, small flaws in teeth of the order of 400 ********m will not radically affect their structural integrity, as predicted fatigue lifetimes will exceed that of the patient.**

- Lawrence Berkeley National Laboratory, University of California, Berkeley