ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1474

Static and time-dependentmechanical behaviour of preservedarchaeological wood

Case studies of the seventeenth century warshipVasa

ALEXEY VOROBYEV

ISSN 1651-6214ISBN 978-91-554-9810-8urn:nbn:se:uu:diva-314266

Dissertation presented at Uppsala University to be publicly examined in Polhemssalen,Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 31 March 2017 at 09:00 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Facultyexaminer: Associate professor Eiichi Obataya (University of Tsukuba).

AbstractVorobyev, A. 2017. Static and time-dependent mechanical behaviour of preservedarchaeological wood. Case studies of the seventeenth century warship Vasa. DigitalComprehensive Summaries of Uppsala Dissertations from the Faculty of Science andTechnology 1474. 52 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9810-8.

Wooden objects have been widely used in the history of humanity and play an important rolein our cultural heritage. The preservation of such objects is of great importance and can be achallenging task. This thesis investigates the static and time-dependent mechanical behaviourof archaeological oak wood from the Vasa warship. Characterisation of mechanical propertiesis necessary for the formulation of a numerical model to design an improved support structure.The ship was impregnated with polyethylene glycol (PEG) for dimensional stabilisation. Allelastic engineering constants of the Vasa oak have been identified and compared with those ofrecent oak by means of the static and dynamic testing. The experiments were done on sampleswith cubic geometry, which allowed obtaining all elastic constants from a single sample. Theusage of cubic samples with orthotropic mechanical properties during compressive experimentswas validated with finite-element simulations. The Young's moduli of the Vasa oak in allorthotropic directions were smaller than those for the recent oak. The shear moduli of Vasa oakwas determined and verified with the resonant ultrasound spectroscopy. The time-dependentmechanical behaviour of the Vasa oak has been studied. Creep studies were performed inuniaxial compression on the cubic samples in all orthotropic directions. The samples loaded inthe longitudinal direction were subjected to different stress levels. A stress level below 15% ofthe yield stress in the longitudinal direction did not result in non-linear creep with increasingcreep rates within the time frame of the tests. The results of the studies in radial and tangentialdirections showed that creep was dominated by the effect of annual fluctuations in relativehumidity and temperature. The weight changes based on annual fluctuations of relative humiditywere measured for Vasa oak and recent oak. The Vasa oak showed higher variations due toan increased hygroscopicity which is the result of the impregnation with PEG. In conceiving afull-scale finite-element model of Vasa ship, not only the stress-strain relations of the materialbut also those of the structural joints are needed. Since the in-situ measurement of joints is notan option, a replica of a section of the ship hull was built and tested mechanically. The load-induced displacements were measured using 3D laser scanning which proved to have advantagesto conventional point displacement measurements. The mechanical characteristics of the Vasaoak and joint information presented in this work can be used as input for a finite-element modelof the Vasa ship for simulation of static and time-dependent behaviour on a larger scale.

Keywords: archaeological wood, compression test, cubic samples, elastic constants, oakwood, barrelling formation, quasi-static loading, resonant ultrasound spectroscopy (RUS),Vasa ship, creep, 3D laser scanning, Time-dependent behaviour

Alexey Vorobyev, Department of Engineering Sciences, Applied Mechanics, 516, UppsalaUniversity, SE-751 20 Uppsala, Sweden.

© Alexey Vorobyev 2017

ISSN 1651-6214ISBN 978-91-554-9810-8urn:nbn:se:uu:diva-314266 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-314266)

M

1964

28

1990

1964

2000 66

FEM model

Geometry

Joints

Prediction (FEM)

Design of support structure

Experiments

Numerical modeling

Elastic and creep properties

0.8−1.2 0.02−0.04

2

3 2 1

1440 −3600− 700 3

2

μ−

1.2± 0.5 2.25± 0.750.4± 0.2 1.5± 0.50.7± 0.2 1.5± 0.75

� 0.025− 0.4 0.05− 0.3718± 5 21± 353± 5 52.7± 536.8± 2 47.1± 69.9± 2 5.2± 2

3 620± 40 353± 603 928± 37 747± 53 1115± 115 1026± 50

3 713± 67 617± 36

ρ =M

V,

M V

ρ =M −M −M

V′ μ−

′

( ) =M

M −M −M

0%

50%

100%

150%

200%

300 400 500 600

PEG

con

tent

(%)

Basic density (kg/m3)

3

3

M < 1000

M710 80

0%

10%

20%

30%

40%

300 400 500 600

Moi

stur

e co

nten

t (%

)

Basic density (kg/m3)

0%

10%

20%

30%

40%

0% 50% 100% 150% 200%

Moi

stur

e co

nten

t (%

)

PEG content (%)

23◦

20− 30

σσ ε

σ = Eε

E

e e e

⎡⎢⎢⎢⎢⎢⎢⎣

εεεγγγ

⎤⎥⎥⎥⎥⎥⎥⎦=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

1E − ν

E − νE 0 0 0

− νE

1E − ν

E 0 0 0

− νE − ν

E1E 0 0 0

0 0 0 12G 0 0

0 0 0 0 12G 0

0 0 0 0 0 12G

⎤⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

σσσσσσ

⎤⎥⎥⎥⎥⎥⎥⎦

G ν γ 6 × 6

ν

E=

ν

E,

ν

E=

ν

E,

ν

E=

ν

E.

E G ν

25 ± 0.051.2 2

L R T

L T R

25

σ

0

4

8

12

16

0 0.05 0.1 0.15 0.2

Axial stress [MPa]

Axial strain [%]

Vasa Recent

ε

εiiεjj εij

νijεjj εii

G G G

ε

40 × 40 2

25×25 2

10mm

0.00

0.10

-0.10

-0.20

0.20

yx

0 0.5 1 1.50

10

20

30

full field

central band

Strain εy [%]

Stressσy[M

Pa]

E1.5

ν νν ν

E G ν

E G

E

0.0

0.5

1.0

1.5

0% 25% 50% 75% 100%

Y

oung

's m

odul

us (G

Pa)

PEG content (%)

Vasa Radial

Vasa Tangential

0

2

4

6

8

10

0% 25% 50% 75% 100%

Y

oung

's m

odul

us (G

Pa)

PEG content (%)

Vasa Longitudinal

EE E E

0.0

0.5

1.0

1.5

2.0

2.5

400 450 500 550 600 650

Y

oung

's m

odul

us (G

Pa)

Basic density (kg/m3)

Vasa Radial

Vasa Tangential

Recent Radial

Recent Tangential 02468

1012141618

400 450 500 550 600 650

Y

oung

's m

odul

us (G

Pa)

Basic density (kg/m3)

Vasa Longitudinal

Recent Longitudinal

ν ν ν

2 922 (37)E 6.75 (1.55) 10.7 (1.4) 8.80 (0.48)E 0.60 (0.15) 1.47 (0.3) 2.60 (0.32)E 0.35 (0.15) 0.89 (0.01) 1.84 (0.34)G 0.62 (0.01) 0.69 (0.03) 1.03 (0.24)G 0.33 (0.03) 0.61 (0.01) 0.69 (0.06)G 0.14 (0.02) 0.20 (0.00) 0.47 (0.14)ν 0.37 (0.02) 0.40 (0.11)ν 0.69 (0.04) 0.90 (0.25)ν 0.30 (0.01) 0.32 (0.05)

E

E E

+0.08 +11 G +0.28 +46 G0.02

G

σa

ε0 ε1 t1 ε2t2 t1 t2

σb = 2σa

σc

εu

t0

σa

σb = 2σa

σc

σ

t t0

ε0t1

ε1t2

ε2t

εc

εu

εb

εa

ε

u t

dudt u

dudt u

0

0

du dt

u

t

tt0

J(t)

J(t)J(t)

J(t)

J(t) =ε(t)

σ

σσ

9 610 20 30

σ0.5 2

20 30 σ5 15

σ

σ

T

T

T

2014 2015 2016 2017Time (year)

16

16.5

17

17.5

18

18.5

19

Tem

pera

ture

(°C

)

50

52

54

56

58

60

Rel

ativ

e hu

mid

ity (%

)

J(t)

ε (t)

15σ

σ

0 500 10000

1

2

3

4

5

6

Creep

compliance

J(t)=

ε(t)/σcreep

×10-9

0 500 10000

0.2

0.4

0.6

0.8

1 ×10-9

0 500 10000

0.5

1

1.5

2

2.5 ×10-10(c)

30%20%15%10%

Time, t (days)

(b)(a)

5%

J(t)1×10−9

T

T ↑ ↓↓ ↑↓ ↑

ε(t) ↓ ↑

2015 2016 2017Time, t (year)

-4

-2

0

2

4

6

8

10

Compressivestrain,ε(t)

×10-3 Radial direction1823

2015 2016 2017Time, t (year)

-4

-2

0

2

4

6

8

10

Compressivestrain,ε(t)

×10-3 Tangential direction564

(a) (b)

TM

17 − 22 ◦

±5±1.5

x

3

ν ν ν

1.5

30 σ

T

TT

Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1474

Editor: The Dean of the Faculty of Science and Technology

A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally throughthe series Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)

Distribution: publications.uu.seurn:nbn:se:uu:diva-314266

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2017